I dug out one on our farm; didn't find anything. I found out later that it was from the depression era and not old enough. (It had concrete for the base, that's how they could tell the age.) I think I know where the older one is, I'm going to try to probe for it next week if we get the rain that we're supposed to and the ground softens up a bit.
The key is SAFETY! I work for a utility, and used to be in a fire company. There is a LOT of instances where holes collapse on workers who didn't know what they were doing. Be careful, and there's a lot of data on the internet. Look up privy digging or outhouse diiging. Good luck! Curt