The thing that the water pump bolts onto

There is nothing under there except air, and if running, an oil-mist.
So it's getting there by; drip, by spray, or migration from somewhere else

OK wait, I'm looking at it backwards; that is the pump side, and so yeah, the housing is perforated. I have not seen that before but the good news is that it is easy to fix. Just remove the pump, and either weld up the pits or clean it up and fill with JB Weld.

But it is possible that the entire cover is pitted behind the pump. I have seen that, I was told cavitation started it, and time finished it. If that is your case then just put up a want-ad; some of us have boxes and boxes of good used parts.