In the case of "Tu me manque", the first thing is to understand that "Manquer" ≠ "To miss"
The word you are looking for is verbe pronominal (plural: verbes pronominaux).
Warning : The following text is pure formal grammar. Is it extremely boring
Some verbs are purely pronominal. Those are usually "Reflective verb" where the pronom and the subject are the same. The pronom do not have a gramatical fonction.
- Je me souviens (I remember)
- Je m'en vais (I am leaving)
- Il se suicide (He is committing suicide)
- Je m'arrange comme je peut (I am doing what I can)
All the transitive verbs can have a pronominal form. But some, such as "manquer (à quelqu'un) are **usually* used in this form.
- Tu me manque (I miss you)
- Tu manque à ta mere (Your mother miss you)
We never say "Tu manque à moi" but the second example shows that this verb is not always pronominal. It is only transitive.
In fact any (really any?) transitive verb can be a "verbes occasionnellement pronominal" where the normal use is the "usual" order but if you use a pronom you have to change the order
- Je regarde cette voiture -> je la regarde
- Il regarde moi (incorect) -> Il me regarde
"Manquer" is the worst possible word to explain this concept.
It can have the 3 forms.:
- essentiellement pronominal : Tu m'a manqué = I missed you (because you've been away)
- not pronominal: Tu a manqué la cible = You missed the target
- occasionnellement pronominal : Tu l'a manqué = You missed it (The target)
The first example is a transitive indirect verb (Manquer à quelqu'un) and the second is a direct transitive verb.
They both can be translated as "to miss" but should be treated as different verbs. Just as "To give"≠ "To give up"
There is even a third meaning : "Manquer de" meaning "to lack"
Je manque d'argent = I lack the money
If you insist on using a pronominal form: "J'en manque"
unlimited source of pun
"Je t'ai manqué" = "I missed you". Both for a loved one or for a missed target
As the proposition (à) do not appear in pronominal form, it is impossible to tell if we use the transitive or intransitive meaning.