Coming from a background in Classics, I initially assumed there’d be a large pool of evidence for (and high scholarly interest in) Byzantine homosexuality, but after a year of graduate-level study I’ve never seen either scholars or historical sources talk about it for more than a sentence or two, usually to say it was illegal. This seems very odd.
Do any modern scholars address this topic? Are there any Byzantine sources that mention homosexual behavior? I know that eunuchs were often accused of homosexuality - though again, I’m not sure in exactly which sources - but presumably this implies that there were bearded parties involved as well? (Do I even dare ask about women?)
I have an excellent book on a very related subject: Eve Levin, "Sex and Society in the World of Orthodox Slavs 900-1700". In absence of better answers, perhaps my reply could offer some related insight, even if considered offtopic. However, Slavic world was strongly influenced by Byzantine tradition. Main primary sources were church codes and confessional questionnaires from which we could infer societal views on Slavic homosexuality.
The Orthodox priests of Slavic world inherited system of Byzantine canon law which made a difference between two types of homosexuals: those who practiced anal sex and those who practiced other forms of sexual activities such as mutual masturbation or intercrural sex. This divide was a legacy of Ancient Greek society.
Anal sex was considered as a severe sin on the same level as heterosexual adultery in the Byzantine law (St. Basil recommended 15 years of church penance), however Slavic church codes were much less severe (penances of two or three years). Punishments were less strict if the transgressors were younger than thirty, with complete absolution if they were younger than twelve (as per Byzantine civil code). Several homosexual experiments during the youth were considered as a light offense – married people however were expected to fulfill their sexual needs with their partner. People who were raped were considered as less guilty than rapists, with several cases of full absolution for the victims. Active partners were punished stricter than passive partners because they were considered as instigators of the sinful activity.
Other forms of homosexual activity were considered as light offenses. Mutual masturbation was punished similar to ordinary, solo masturbation. Intercrural sex was considered even less of a sin, and those who committed it could be accepted into priesthood. Two men kissing “with desire” would incur only a slightly heavier punishment than man and a woman kissing – 40 days of church penance with one hundred prostrations. Inciting another man to sex was regarded the same as inciting a woman.
Much heavier punishments were reserved for those who would assume feminine looks, for example by shaving a beard, which could be punished by excommunication. Orthodox believers thought that men were created in God’s image so any change in their look which made them more feminine was a blasphemy.
The problem with homosexuality was not in “unnatural” attraction between same genders, but in disruption of common societal gender roles. That is why mutual male masturbation was regarded less harshly then penetrative sex – by masturbating, both men kept their “male” roles, whereas during the sex one man needed to assume the female e.g. bottom position.
In any case, Slavic church authorities were noticeably less harsh towards homosexual activity than their Western counterparts. The worst case of homosexual activity was punished equally severe as a heterosexual adultery – a penance of several years with fasting and prayer, as opposed to death penalty in the West. Dušan's Code and Russkaya Pravda, important legal documents of their age, disregarded homosexuality completely. Monastic regulations also had no mention of homosexuality, which could lead to conclusion that such activities were confined to monastery walls. However homosexuality could be noted in everyday life. Samuel Collins, an Englishman who visited Russia in 17th century, noted that Russians are “naturally inclined” towards “Sodomy and Buggery”, which could mean that Russian society of that time was tolerant, rather than inclined, towards homosexuality. A separation of Russian society into male and female spheres could only increase the possibility of sexual contacts.
Lesbian activity was not considered as a serious transgression. Sexual act between adult women was ranked as a more serious sin than mutual male masturbation, but less serious than male anal sex. Interesting to note was that greater punishments were intended for ladies who would take the male role during the sex, for example by “straddling” (correct translation/meaning is not exactly clear) the other woman.
There is also an interesting angle on female homosexuality: it was often connected to pagan rituals and customs. Women who participated in homosexual activities were named “women who insult the Lord” which was an expression often used to denounce female pagan leaders. They were also accused of worshiping the female pagan spirits through lesbian activity. Lesbian games between young unmarried girls were common in 17th century Russia. Such games would often take form of wedding reenactments, and were tolerated with a slight disapproval because they were considered as a preparation for a married life without the risk of losing virginity or premarital pregnancy.
Source: Eve Levin, "Sex and Society in the World of Orthodox Slavs 900-1700". For chapter on homosexuality, she used exclusively primary materials such as medieval church codes, which makes recommending secondary sources problematic.
Since you mentioned eunuchs in particular, I know of some scholarship on the eunuch/homosexual connection in Byzantine society which may be of interest to you. Kathryn Ringrose in her book The Perfect Servant: Eunuchs and the Social Construction of Gender in Byzantium discusses this:
As Michel Foucault has so ably shown, we must not assume that other societies operate using our categories, no matter how obvious and basic they might appear to us. We must avoid the tendency to ascribe reflexively to the medieval world our modern assumptions about sexual categories and behaviors that seem familiar at first glance, or to make quick assumptions about the sexual nature of a society in a world that was very different from ours. Thus it would be anachronistic and illogical to assume that the Byzantine category of eunuch was in any way analogous to the modern category "gay" despite the pejorative traditions shared by both. It is true that some Byzantine sources do refer to a category of eunuchs who are "eunuchs by nature.” For example, in the tenth-century Vita of St. Andrew the Fool we find that such a eunuch befriends the saint's disciple, Epiphanios. This eunuch is young, and the saint accuses him of being a sodomite. In the Vita of St. Basil the Younger there is a long diatribe against the powerful court eunuch, Samonas. He is called a "eunuch by nature", and accused of engaging in acts of sodomy. [...]
I suspect that "eunuch by nature" may be a code phrase sometimes used to refer to those castrated men who actively seek out sexual relations with other men. While such references allude to sexual acts that we associate with male homosexuality, there is nothing to suggest that the gender construct for eunuchs can be usefully compared with modern concepts of homosexuality. In a more general sense, there is little evidence that individuals in the Byzantine world were placed in gender categories primarily because of sexual preference of any sort [...] (pg 22-23)
So it's the usual distancing from the modern concept of homosexual identity, but there is some connection between eunuchs and sodomy (aka homosexual behavior, just not identity.) The book is very good if you haven't read it. I highly recommend it, I think it's one of the best pieces of eunuch scholarship ever written, straight up. (Poached from this old answer)