okej! i’m more knowledgable about china, but afaik there’s an ongoing debate on whether byzantine eunuchs were considered a third gender identity or simply effeminate men, which you might be interested in chinese eunuchs were not rlly viewed as a third sex until influenced by western orientalism

in the early days people playing the role were intersex (around the zhou dynasty), then castrated prisoners were used, in the eastern han the use of eunuchs in certain offices was fully institutionalized, and the practice of selling children into the palace became more common in the han dynasties