This question, which I'd certainly characterize as a higher level thinking question, has led me in endless circles, on dead-end tangents, and finally, to
the conclusion that I lack the kind of higher order thinking skills required to fully answer it.
This is evidenced by the fact that, concerning the meaning of brasse-camarade, I have previously formulated many conflicting opinions, including one opinion/"answer” concentrating on the English notion of “movement”; then a second on that of “confrontation” (both of which are re-posted below in reverse order); and now (but certainly not finally) a third:
Although generally relevant as it stands, I now feel that (in both English and French) “confrontation” is lacking something and should be narrowed, especially in political contexts, to capture the notion of "confrontations between members of a group," which is captured well, I think, in English by The American Heritage Dictionary’s first, slightly figurative meaning of “in[-]fighting”:
“1. Contentious rivalry or disagreement among members of a group or
organization: infighting on the President's staff.” …
… which in turn, according to some examples from Reverso Context, could be translated as “querelle/lutte/conflit intestine/interne” and to the figurative extreme, perhaps even as lutte fratricide as I believe Honoré Mercier was using it in his memorable words: «Cessons nos luttes fratricides! Unissons-nous!»
(from Delbusso Editeur)
Although probably totally coincidental, it is perhaps interesting to note that even the more literal meaning of infighting in English (i.e., “2. Fighting or boxing at close range” = “close combat” = “corps-à-corps?) could be seen as corresponding a bit with “brasse-camarade” when used in contexts involving actual contact, as in hockey, and to the extent that corps-à-corps is a valid translation, somewhat with the important notion of “[à] bras-le-corps” discussed in this good answer.
Finally, regarding possible origins of the term at issue and/or possible explanations of its attributive use in Le Phare, please see my thoughts on those points scattered throughout below.
(cf: possible translations of the noun "infighter," including, from Word Forum, ennemi intérieur, which I don't particularly like in the Le Phare context, or in any context for that matter)
(original answer as first posted [with some of its grammar mistakes corrected])
In spite of all the notions and suggestions found way below ... ,
(in what was originally designed to be my answer, but which I’m keeping nonetheless because of some overlapping cross references (and NOT as it might appear, just to make this a longer and harder read than it needs to be because that ship sailed long ago with just this new “answer”)
... upon further reflection, I think the best single-word noun that could replace brasse-camarade in both of the question’s particular examples would be confrontation in CNRTL’s sense # B(3)(c):
“À l'idée de face à face s'ajoute celle d'affrontement (another
possibility?), d'antagonisme, de conflit; …,”
which is the French sense that most closely resembles the meaning that I most often associate with that word in English:
“Rien de tel qu'un peu de confrontation en fin … .”
“On vous demande de faire votre confrontation [avec vos membres].”
(although like «faire votre brasse-camarade» (see way below) the votre seems weird to me and either:
“On vous demande de faire une/la confrontation » or
“On vous demande de confronter vos [membres]”
would probably be more idiomatic)
For the use of « brasse-camarade » as a noun representing a person with [a] certain characteristic/s, such as in « Il était un brasse-camarade invétéré » from Le Phare and mentioned in the comments, “confronter,” “confrontationalist,” and even “confrontationist” exist as nouns in English to describe “a confrontational man/fellow.”
In French, however, such attributive forms (confrontat/aire/eur/rice or confrontation[nel]iste) don’t seem to exist and even if un homme confrontationnel or homme de confrontation might be understood in French, the fact that they get respectively zero and only 10 hits on google.com is perhaps good evidence that it’s just a notion and construction that’s been borrowed from English.
So for a suggestion somewhat related to confrontation for that attributive usage in Le Phare, looking back to CNRTL’s sense # B(3)(c) for confrontation, there’s “the idea of antagonisme,” which could lead to antagoniste (also from CNRTL).
However, even though it doesn’t totally jive with my confrontation theme and theory (and without knowing the full context of the description from Le phare), I think agitateur would be even better, i.e.:
“Personne qui crée des troubles, le plus souvent à des fins
politiques, sociales ou révolutionnaires”
also from CNRTL
(note also the word’s connection with the beer brewing/brasserie industry, which makes me wonder now if agitation (mentioned in the question and in a “Random” comment directly under it) wouldn’t be better than confrontation in ALL the contexts, but it’s too late for that for this great question has already sent me on too many tangents and exploring agitation any further would probably just give rise to several more to pursue!)
Regarding possible origins, the similarities mentioned [still] way below between brasse-Canayen and brasse-camarade at first led me to feel that perhaps camarade at some point began replacing Canayen because the former was seen as a less offensive way to refer to oneself and to one’s fellow sufferers of such treatment (being shaken/pushed around).
However, being unable to find any indication that Canayen is/was considered to be offensive, I considered the following possible reasons (all pure conjecture) for what I still believe could be an instance of replacing/shifting from one word (Canayen in this case) with/to another one (i.e.,camarade):
1) To create an expression that would be more universally applicable (not just to contexts involving French Canadians and somewhat more universally understandable (to the extent that at least knowing the meaning of Canayen would not be required to understand it).
2) To create an expression that would avoid using an arguably joual term (especially one like Canayen that meant/means “Canadian French”), which could be seen as consistent with «La Révolution tranquille et le joual emballe, 1960-70» described (as I interpret it) in Chapter 9 of Chantal Bouchard’s La langue et le nombril: une histoire sociolinguistique du Québec as a pivotal moment when a renewed pride in the nature of their French caused the people of Québec to move away from joual, which over the years had become, perhaps wrongly, synonymous with la langue canadienne-française (especially when called canayen) and move toward being proud Francophones speaking Québécois (not to mention that this also permitted them to avoid using the word canadien or even a corrupted version thereof, when referring to their language and to their fellow Québécois, i.e., their fellow camarades).
Alas, the appearance of “brasse-camarade” used attributively in Le Phare pre-dates the Révolution tranquille mentioned above by at least 10 years, so there’s another tangent pursued in vain, but as mentioned in a comment, this particular early use could possibly be borrowed from the English “brass fellow” with camarade being a reasonable substitute for “fellow.”
Or perhaps even a transformed borrowing of the hyphenated adjective “brass-knuckle [tactics]” for use as a noun.
(cf this rather clever name for a brass quintet from the ensemble’s website)
If such borrowing does explain the usage in Le Phare it could certainly be seen as the precise origin of the term as it’s used today, but if it was a one-time, unrelated act of borrowing, the Révolution tranquille angle could at least help explain any accelerated use of the term that followed that revolution.
(for possible further tangents to pursue (or with which to question my “conclusions!), see this interesting juxtaposition of “des prises de bec, des différends, [and] des brasse-camarades” in paragraph 2 of a Le Robert dictation exercise and the last commentaire des difficultés on the bottom of page 2 found at belfortho.fr;
(as well as the following Google hits for the term’s two plural forms: “brasse-camaradeS” and the questionable, yet more popular “brasseS-camaradeS”;
(and finally here for what appears to be Larousses’s official entry (including the plural) for brasse-camarade from a somewhat random looking Facebook “page.”)
(end of "new" answer)
(heretofore un-posted original answer below)
In light of their similar hyphenated structures (“brasse+[-a noun that could be seen as representing a compatriot or a sympathetic fellow member of a group]") and the identical use of “remue-ménage” in both this Quia entry for “Brasse-Canayen” and in the one cited in the question from Wiktionnaire (#1) for “Brasse-camarade,” I’m tempted to conclude that the meaning of the two terms is identical and that examining the uses and meaning of one can help explain the other.
Further evidence of a connection between the two terms is that they both have variations expressed in identical forms having identical meanings, to wit:
se faire brasser le camarade from a Trip Advisor review of a roller-coaster ride
and se faire brasser le canayen from Isa’s Blogspot description of similar amusement park rides.
Both of the above usage examples are, in my eyes, describing the same movement and motion, i.e., a physical shaking/jostling or the feeling of being literally shaken/jostled about from left to right, just as, according to my interpretation of the entry under “barouette” on Angelfire.com, “se faire brasser” all alone would mean.
All that to say that I feel that both of these hyphenated expressions (and especially their “se faire brasser” variations) are based on the literal sense of the notions of movement and motion in general and, in particular, movements/motions that would be described (in English) as “jostling” or “shaking” (and in spite of James Bond’s preference re martinis, perhaps even “stirring”!)
Therefore finding their meanings (in English) when encountering them (especially the hyphenated versions) used figuratively in French requires, for me at least, finding relevant figurative English uses of “jostling” (e.g., “jostling for position”) and/or “shaking/stirring (e.g., “shaking/stirring things up”) (or even just “a shake-up,” but see below) and then finding possible French equivalents for them.
“Jostle/jostling for position” could lead in French to “bousculade” (mentioned in the question) or from Reverso, “jouer des coudes”, which I think could fit both figuratively (maneuvering to gain an advantage) and literally (throwing elbows) in the hockey example:
“Rien de tel que de jouer des coudes un peu en fin … .”
Granted, the notion is being proposed as a verbal phrase because I’ve found little or no instances of its use as a noun (i.e., “ Rien de tel qu'un petit jeu des coudes en fin… . ”)
Using Reverso’s “context” tool, “Shake/shaking [things] up [a bit]” as a verb led me to 4 instances of secouer [un peu] les choses as a verbal phrase and one instance where the phrase is used with the verb “remuer” (as in le remue-ménage).
As for Reverso’s entry for “stir things up” (= donner un coup de pied dans la fourmilière), perhaps 007’s preference is a bit too strong, but then again it, along with all of the verbal phrases mentioned above, could work well enough in many political contexts:
“On vous demande de donner un coup de pied dans la fourmilière.”
“On vous demande de secouer/remuer [un peu] les choses.”
“On vous demande de jouer des coudes (figurativement).”
On the other hand, Reverso’s entry for “Shake-up” as an English noun could lead to [grande?] reorganization, which seemingly corresponds with Wiktionnaire’s 2nd meaning for the term at issue, but the inclusion of grande conflicts with my understanding of the extent of changes made during a “shake-up” in English (and during a brasse-camarade in French) leading me to conclude that perhaps reorganization, especially in light of the curious votre reorganization that would result, is not appropriate in the particular political context mentioned in the question.
(end of old/original answer and with it the end of this entire[ly too long] post)