Gender identity

I don't get gender identity.

I am a cis-male but if you transplanted my brain into a cis-female body and everybody started calling me a woman I wouldn't mind. I would even start calling myself a woman because that's what I would be. I have never doubted that I am a man though, I just don't understand what gender identity is supposed to be.

From what I understand gender identity is some kind of strong internal sense/feeling of what your gender is but I seem to lack that. Is this normal?

I don't mean to come off as transphobic with how I wrote about being male/female, it's just that my gender just seems to depend on what body I'm in.