It's something I don't think I have ever bothered looking up since then, but I stumbled across an article today from the Wellcome collection The castration effect, and it notes as follows:
Early Assyrian and Chinese civilisations transposed this knowledge to humans: boys born in poverty would be castrated and sent to work under the yoke of the state in the imperial household. (In China, both penis and testicles were removed – these ‘three treasures’ were pickled in a jar, brought out for special occasions, and buried with the eunuch.)Well, I wonder on what special occasion a eunuch would bring out his pickled genitalia. Birthdays, perhaps? Anyway, it would seem the method used all depended on the time and place.
Someone (apparently a historian) at Reddit gives more detail:
The interested reader can go to that link and read in detail the gruesome clean cut method used by the Chinese. I wonder how many didn't survive it...Anyway, here’s Eunuchry 101. There are two basic types of eunuchs in history, “clean-cut” (no penis or testicles) or just a removal of the testes. A simple removal of the testes is historically the most common sort. There’s a third type where the penis was removed but the testicles left, but it’s only referenced in a few places for Islamic eunuchs and seems to have been a very limited thing, and there’s really no reason to do it like this other than punishment.For clean-cut eunuchs there was basically only one method, cutting it all off in one go which I described for the Ottoman black eunuchs in that link, and here’s the Chinese version from G. C. Stent who is probably our most reliable Western reporter: