It's a southern thing. In fact, I'd never even heard the expression until we started fraternizing with southerners. I'm not talking about mountain folk, people from Kentucky, east Tennessee, and such. I'm talking about southerners. People whose great-great grand-daddy seceded from the union and they haven't gotten over the fact that it didn't stick. People who regularly vote Republican. (Yes, believe it or not, there are people like that.) Real southerners.
A hidey hole is somewhere your cat goes 10 minutes before you need to leave for the vet's. You cannot find them. That is not just an expression; it's a fact. You CAN NOT find them. By definition. You turn the house upside down, look in places that weren't even places a half hour before, you rattle the bag of treats, you place the other cats under a bright light and give them the third degree. Nothing. They're in the hidey hole.
I probably should consult with Stephen Hawking, for I suspect hidey holes have something to do with the space-time continuum, whatever that is. Hidey holes may actually exist only in concepts of theoretical physics, but cats, being far superior to humans, move freely in and out of them.
Here kitty, kitty!