How do you solve a problem like a mystery switch?

Start by opening them up and seeing if they've been bypassed. Sometimes people eliminate a switch, and then don't bother removing the switch because they don't want to be left with an empty hole. If you find a bypassed switch, un-bypass it.

Some switches actually switch power to a receptacle. This is often done instead of an overhead ceiling light, because that saves the builder a couple of dollars. There's a complication: As you know, most US receptacles have 2 sockets. The sockets can be split to be separately controlled: if you ever hear something about "tabs" on sockets, that's what that's all about. It's common to split and have one socket switched and the other always-hot. So you need to check 'em both... on each recep.

Sometimes, novices replace receptacles (they don't like the color) and they don't even realize that tabs are a thing, so they don't break off the tab like the old one was. This will have the effect of defeating the switch. Spotting these is a bit of a trick, and the only way is to open up the receptacles and look for odd wiring.