what makes an 'ideal you form in your head' a 'gender identity'?
You and I both recognize that enforcing sex essentialism is wrong (you have loudly accused me of being sex essentialist, in a context which implies it is in some way bad).
This would be "placing expectations on others", or some such, as LD considered gender (in the post I was replying to, in fact to disagree with LD).
I might note that reducing it to the genitals would be an essentialization again of whatever it is gender is expected to be. Yet again this is sex essentialism!
This corners gender to an image not enforced by others or essential to some proxy (gonads) but
something formed from within, where behavior happens. Gonads don't create behavior, they at best allow hormones to place weight on the thing that does: the brain.
When observing how people treat matters of gender, they say that the pronouns are theirs; that they are the users of the pronouns, not that the pronouns are the pronouns for "all people like them".
Where would such a thing, such a model for being come from but from within, if we are to reject
essentialism, this idea that one thing (behavior) is
essentially linked to some other thing (gonads or w/e)?
When I say "gender" that is what I have always meant by it, and the way people use words is what gives them meaning. Using "gender" that way is enough to give it that meaning.
It is a common enough usage that at least three other posters liked what I had to say on the matter.
What does calling it a gender identity add?
In some ways it's what calling it a "gender identity" subtracts. It subtracts a lot of more complicated words and compresses them into a two word term for "subset of self-image ideals with regards to posturing with regards to sexual and sex-adjacent behaviors".
It lets me say "an identity" (a self-image ideal) with regards to "gender" (the subject of posturing with regards to sexual and sex-adjacent behaviors). There may be ways to say that with less than that many words but certainly no better way to say it than to say "gender identity" or simply just "gender".
It comes down to whether the person who holds the ideal declares this ideal that they pursue "he/him", "she/her", "they/them" or something that is perhaps unreasonable at this point in time owing to the glacial rate at which culture changes.