Here are the Chinese characters for 남사당:
Looking at the Chinese characters, the literal meaning of 남사당 is "a male Buddhist temple group." Does that make sense? And, if the 사 was supposed to mean "eunuch," then the literal meaning would be "male eunuch group," which makes a little more sense, if you can accept that removing a guy's gonads makes sense. However, 사 can also mean "village," so maybe 남사당 originally meant "male village group"?
Another strange thing about 남사당 is that the 당(黨) in 남사당 means "group," which means the word should mean "a group of itinerant male entertainers," instead of just "one entertainer." If that were the case, then it should be redundant to add 패(牌) to the word since 패 also means "group."
While reading about 남사당, I learned the word 땅재주, which means "a somersault," "a handspring," or "a tumble." 땅재주 is a compound word. 땅 means "ground" and 재주 means "talent." Also, 모로 땅재주 is "a cartwheel." 모로 means "sideways."