This is a great question and I'd love to hear how other historians approach this conundrum. It can be really frustrating (as a person who falls under the LGBT category, as well as as a historian) to run up against those areas in history where we just don't know for sure what was up with a specific historical figure, but it might be helpful to think of what can be learned even without 100% certainty. Even if documentation is scarce or primary sources are especially biased, the nature of that documentation and the biases on display can still tell us a lot about contemporary attitudes. Something I run into a lot is eras and areas where documentation of same-sex sexual activity is limited because it's drawn predominantly from court records -- that doesn't necessarily tell us much about same-sex sexual activity that wasn't escalated to the attention of the legal system, or same-sex sexual activities that flew under the radar, or same-sex sexual activities that for whatever reason went undiscovered. Nor can it necessarily tell us much about what participants thoughts about themselves -- whether participants viewed themselves as different from those who didn't participate in same-sex activities and if so, how. But there's still a really useful backbone of data in there -- how acts and their participants were described, which aspects were focused on, the social class of participants, verdicts and defense arguments, etc. That alone won't give us a complete picture, but it's something, and as long as historians clearly establish the parameters of their work (I've fallen afoul of that myself -- trying to generalize too broadly about LGBTQ lives and experiences from sources that only really reflect a subset of that community in a certain place) it can still help excavate one aspect of a poorly-documented past.

The same could go for other source materials -- medical theories of homosexuality, or military records pertaining to same-sex behaviors, or newspaper accounts pertaining to gay social events and high-profile gay people, or even the holy grail of personal correspondences and oral histories. All these sources have limitations, and they can't eliminate all ambiguity or answer to all the facts a modern historian might prioritize, but even reckoning with uncertainty and incomplete data we can begin to fill in some of the traditionally blank spaces of historical study.

At this point, there have been decades and decades of study dedicated expressly to gay, lesbian, bisexual, and transgender history -- both individual lives and studies of communities, movements, and subcultures. That's a lot of cool stuff to build on, and I'm really lucky as a historian in almost-2019 to be standing on the shoulders of giants here. There's also a lot of value in studying historical phenomena that are more LGBTQ-adjacent than they are LGBTQ proper, as well as individuals and historical phenomena (Byzantine eunuchs, Boston marriages, Renaissance Italian castrati, Elizabethan boy-players and Jacobean viragos, etc.) which can only tenuously be called LGBT but still shed light on historical patterns of difference in gender and sexuality. Basically, historical research that chips away at the idea that the past was a single unexamined and homogenous blob (where everyone acted and thought exactly like the modern-day assumed default) can be a boon to LGBTQ history and in my experience to LGBTQ historians as well. Scholars of LGBTQ history have to reckon with a lot of uncertainty, but I don't think that such uncertainty is necessarily a stumbling-block to all research and conclusions. It's just part of the playing field, sometimes a very frustrating part, but it can shed some light about the complexities of historical mindsets and serves to remind me of my own biases and implicit expectations.

On another note, there are some historical figures who are generally agreed to fall somewhere in the loosely-grouped collection of LGBTQ identities, but where there's not a consensus as to which identity they'd be best classed under. These disagreements can get pretty ugly, and even at their most civil and factual, it's still pretty painful given the relative paucity of historical representations of LGBTQ people (relative to assumed-not-LGBTQ people, anyway) to hear or to tell someone else "so sorry, but this dead famous person isn't x, like you, they're y, like me." I don't really have ownership of someone whose historical experiences might resonate with me and my own identity as much as they resonate with someone else of a markedly different identity. As tempting as it is to lay a decisive claim to a certain figure as part of establishing the validity and historical precedent of my own identity, sometimes things really are ambiguous, and my opinion as a historian is that it's more useful to acknowledge that ambiguity and its multiple facets than to spill lots of ink making a case for why Q. Dead Historical Figure could only and exclusively have been precisely one thing. Even in the modern day, with a plethora of self-descriptors and subcultures available to so many people, identity isn't as cut and dried as that; I think it's less than helpful to litigate and re-litigate who "gets to" identify with a certain figure. /climbs down off soapbox, sets down hobbyhorse

You might try this reply by u/WhyCantchaBeTrue: https://www.reddit.com/r/AskHistorians/comments/9nalwp/how_do_historians_decide_if_someone_was_really/

Of course studying "LGBT history" in ancient times is a bit like studying the history of the american democratic party in ancient times. What we conceive of as "lesbian," "gay," and "bisexual" identities only exist in the context of our own "straight" default identity (likewise constructed). Men who penetrated both men and women would be bisexual in our own time but equivalent to the default male sexual identity in Roman times. Men who were only penetrated by women would be equivalent (if such a word can be used) in Roman times to a gay male identity in our own time.

I've studded lesbian and gay subcultures in the UK during the 18-19th century. Some good books to read on that topic would be "mother claps molly House" by Rictor Norton (mostly about male gay bars in the 18th century), or the diaries of Anne lister who was a lesbian woman who lived in 18th century York (its one of the only first hand accounts of a lesbian women at the time). I tend to look at lgbt history as a study of the culture rather than individual people as there are very few first hand accounts and most of the sources are criminal records of people arrested for being gay.

In terms of individual people historians tend to avoid that because its hard to judge. For example it's theorised that Alexander Hamilton had a gay lover based on some of his letters but it's very hard to tell because people had a more poetic way of speaking at that time. I'd recommend http://rictornorton.co.uk as it has a wide collection of primary sources on the topic including Hamiltons letters.