This is a topic that fascinates me.
Some of the older inventories that supposedly test gender on the spectrum from typically female to typically male operated on the obviously flawed assumption that maleness is defined by ability to do math, understand spacial concepts, visualize data and mathematical relationships, visualize geometric relationships, etc. Conversely, female was characterized by ability to remember musical themes, interpret emotional states of others, care about needs of others, write and handle verbal or language based reasoning and ideas. The questions are written in such a way to classify in an exclusive manner, that is you're either male or female, not allowed in the structure of the tests to be essentially strongly capable in aptitudes characteristic of both concurrently. Obviously an anachronism, not accurate, not relevant.
I, for one, have aptitude for all of these things, both the male and female by these criteria. I have male and female faculty colleagues and collaborators who similarly able to do high level mathematics and scientific research who would similarly score high in both maleness and femaleness using these criteria. The vast majority are surely cisgendered men and women. My own situation is that I play the typical externally male roles, behaviors and mannerisms. I am sure no one I work would suspect I identify as female internally. My suspicion is that the ambiguity in assignment of simple male vs. female gender identity increases to some degree with increasing intelligence and/or education.
This goes to underscore the point that gender is not a social construct or defined by a small set of superficial external characteristics.
