Sorry to frame this as a response to you, I think maybe it was somebody else who said something that seemed to imply it.
In any event, your clarification of the issue here is on point.
It’s an interesting question to ponder. We don’t remotely understand consciousness, of course. But if consciousness is an adaptation, it’s the effect of consciousness on influencing behavior that’s adaptive. And it’s probably a reasonable speculation that if less intelligent animals are conscious and self aware to some extent, that it would probably work in the same general kind of way as humans. That in your example of a peacock his conscious mental state would involve some kind of positive feedback from adaptive behavior to his conscious mind - “it feels right and natural for me to behave this way”. And if he’s self aware he’d surely have some kind of sense that he belongs to one of two categories in his species, since adaptive behavior toward his own category (competitor) is generally quite different from his behavior toward the other category (mate or potential mate).
However… I think it’s also quite possible that the specific transgender type of phenomenon might only occur with regularity in humans, with our uniquely complex brains and social structure.