Does that pipe recirculate water to the pump and waterfall, or control the water level?

@skip1909, it doesn't seem to do either. I suppose it could control water level, although I've never filled the water high enough that it goes into the pipe, and I'm not sure where the water would come out if it did. Perhaps that's the purpose of it, though (?) It definitely doesn't seem to have anything to do with the pump, as the pond was functioning when we bought the house many years ago, and it just used (and still does use) a submersible, plug-in pump that sits on the bottom of the pond and recirculates water through tubing connected from the pump up to the waterfall spillway. The pipe isn't involved with that function at all. It's a mystery!

Overflow pipe

You could paint it the color of the rocks, including the inside as far as you can reach, so it blends in better.

It looks like an over flow pipe to me also. You may not fill the pond water that high, but mother nature may .

I would have guessed overflow, too ... except that its opening appears above the height of water containment. In other words, water would leak out everywhere else before it could ever reach the overflow. If you have a small compressor or a portable air tank, find a way to attach it (pvc fittings & tape, etc.) & use compressed air to see if you can detect air escaping somewhere else.

This is a real mystery. :) I would go with an overflow pipe too. It looks like it might be a tiny bit above the top of the pool side. I saw the coupler too, and wondered if the bottom has a coupler too. Not sure what that would mean, except you could unscrew it and put something shorter or taller on it (or close it off). Is the previous owner still around who you might ask about it? That's a neat old cement pool. I can remember in the 1950's, walking home from school and someone had a small cement pond and we would stop and look at it.

If a squirrel is launched, be sure to post the video :-)