Re men — I know it’s a slight diversion: there was plenty of male cross dressing going on across a range of historical periods in the past, but of course the antecedents of it were very different — either understood as part of a male-male erotic subculture (as in Georgian Molly-houses), or as part of a quite acceptable-on-the-down-low pseudo-Greek experimentation for boys and young men with pederastic relationships with older men. (Often these took the model of the young man as coded as pseudo-feminine when he is in his youth the object of older male desire. Such young men would not have course necessarily had a concept of exclusive same-sex attraction, and might generally have gone on to have socially acceptable heterosexual marriages.)
There was also a tradition of imagining cross-dressing as a form of youthful high jinks for the aristocratic classes — this might also be in a kind of continuity with boy players on the stage, as it was often about theatricality and a sort of sexy pastoral misrule — one of the earliest English proto-novels, Sidney’s The Countess of Pembroke’s Arcadia, has a long section where the two main male characters cross-dress as pastoral maidservants in order to get close (in a sexy titillating way) to the virginal female aristocratic objects of their affections (nightgowns blow up, glimpses of skin are had, the young men dressed as women get hot and bothered, and so on).
There’s a lot of male crossdressing in bawdy plays and texts from early periods onwards, much in the prototype vein of traditional crossdressing comedy drag acts; similarly bed-tricks and so on in later verse and plays. So there is definitely a tradition of men cross-dressing for comedy, larks, theatricality, sex (of various kinds), and so on; but it’s genuinely very hard to find examples of men who genuinely appeared to want to live as women — rather than men engaging in role-playing certain aspects of submission or femininity as a part of erotic same-sex or theatrical/literary culture.
As is ever the case, before the idea of the “homosexual” started to appear in something akin to its modern form at the end of the 19thc, it’s a difficult job enough decoding the different historical understandings of same sex male erotic relationships. Masculinity (and male-male friendship) was often coded very differently in earlier periods, so disentangling what is culturally an aspect of erotic (versus non-erotic) same sex interaction is hard enough already.
Often one of the few ways of expressing same sex erotic attraction was through gender performance; so it’s likely that for men, cross-dressing or performing some aspect of “femininity” was most often a signal of same-sex desire/preference, rather than a desire to “become” a woman (which would not have culturally been an attractive prospect for the most part).
However, it’s probably impossible to tell for certain. There were certainly men throughout history who looked perfectly “normative” to wider society, but performed really very unconventional sexual roles in their personal lives (though it tends not to be until a little later in the nineteenth century that they or others tended to write in lots of detail about them. Look up for example the Arthur Munby/Hannah Cullwick diaries for some historical people with very unconventional sexual lives!)
Again, though, it’s extremely hard to disentangle what might be identity from orientation from sexual preference/fetish from personal circumstance from the desire to play with/upend cultural norms for a myriad of other reasons. All of those things were probably bound up together in complex ways, as they are today — but the one thing we do know is that (Foucault!) the complex configurations of the past were not at all the same as the ones we have today, so we’d be mistaken if we simply overlay our own ideas on the past and pretend they’re the same.
It’s as fine artistically to imagine Joan of Arc as nonbinary as it is to imagine Shakespeare as a TV scriptwriter, or that Julian of Norwich was actually an immortal vampire with a nut allergy — as long as there’s no attempt to pretend it’s historically accurate in any way; or some kind of politically significant uncovering of “the real story of trans identity”. That’s just nonsense. (And those writing the programme notes seem not to have understood that people in the past were well versed in rhetorical and imaginative phrases, and that they did not necessarily think that putting on different clothing actually changed the truth of your nature — it’s a quite routine rhetorical and figurative trope, and not an expression of a literal belief of the time.)