Presumably the sign meant to say something along the lines of pelvic, or vaginal examination, or whatever the proper English medical signage should be, which would have the correct connotation, but instead they only picked a word with the same denotation.
Wait, is goober slang for vagina somewhere? In the us south it's just peanuts, and occasionally a kid friendly term for a silly person. I can imagine it being used as a term for a penis and/or balls, but ive never personally heard it.
It needs to become so standard that one day an old man will call his grandson a goober and the whole family will be mad at him. He somehow missed the memo.
Also, later seasons of the Andy Griffith show will be up to 100x as funny.
People will be watching this old show and then suddenly the goofy vagina character shows up as a permanent resident.
The funny part is that 阴道 (yīndào) is a bit euphemistic - the meaning "vagina" is from something like "female channel", but also translates as "concealed path" and carries connotations of the moon.
It's actually the same "yīn" as in "yin-yang" and the same "dào" as "Daoism", so "cunt" probably wasn't a great translation in terms of cultural nuance.