Engine Summer

Oh, huh, there's a term for what you are describing, if you want one. Body Integrity Identity Disorder. NB: I advise caution in googling this. You will find 50% disturbing stories of people self-amputating parts of their body they can't integrate as part of themselves, 45% people saying ableist stuff about this, and 5% interesting information. I wrote extensively about this in law school as it raises all sorts of issues of identity, self-determination, medical ethics, disability fetishization, etc. etc. It was for several decades spoken about in the literature in the same breath as transgender desires, and pathologized similarly. At some point in the past few decades, a few people seem to have argued strenuously that the two had nothing to do with each other, which I have no ground to judge either way, but the result seems to be a reduction in pathologizing transgender identity and no reduction in pathologizing body integrity issues.

Anyway, yes, that's the weirdest side-effect I've ever heard of.