> Also, this theory would suggest that eunuchs, self-identified men who voluntarily undergo gonad removal, would generally come to identify as women, but this is not the case
Not necessarily, there are other possibilities, for example the mechanism might not be lack of male hormones, but elevated female hormones, or environmental contaminant analogs thereof.
If true, it would likely be much more complicated than simply hormone levels. Many trans people have their hormones tested before HRT[1] to establish a baseline and then again after starting to dial in the correct dosage. If it were that simple, baseline testing would reveal it en mass.
The hormone panel is typically T,E1,E2, but human hormonal pathways are complex[2] and not fully understood. There are, for examples, hypotheses involving "backdoor" pathways that should/could be verified, but aren't due to lack of research funding directed toward an admittedly small group of people.
1. That's not to say all or even most, but it is very very common.
Not necessarily, there are other possibilities, for example the mechanism might not be lack of male hormones, but elevated female hormones, or environmental contaminant analogs thereof.