If you see coolant on the top of it; that didn't come from the housing. It came from above the housing like that bypass hose, or more commonly, the T-stat housing.
Do a pressure test.
The only place that housing can leak coolant, is from the tubes that transfer coolant between the pump and the block, which do very occasionally rot. But more likely the coolant is leaking at either of the two long bolts that screw into the block that are open to the inside of the block.
If you take it apart , the cover is probably just fine, or will clean up just fine. Besides; it's aluminum, a couple of minutes with the welder and a file and she's good to go again..
If you do take it apart;
be advised
that each of the 4 long bolts is likely to be a different length, and needs to go back into the correct location. It is possible to put the longest bolt in the wrong hole and drive it into the outside of #1 cylinder and to crack that cylinder, sending coolant forever into that cylinder.
