Thanks for the responses. The Wikipedia citation combines the beginning of the quote I shared from Moe's autobiography with another story which immediately follows it. It says:
"Oily To Bed, Oily To Rise," another 1939 goodie, was -- what else -- an oil well picture. The plot had us in one scene, trying to repair a water pump. After many attempts, I took a screwdriver, knelt down, peered into the mouth of the pump, and jiggled the screwdriver inside of it. Gazing up the opening, I jiggled again and then looked up a third time. Suddenly a blob of assorted gunk got me right in the eye again. And again it took hours to clean me up for the next scene.
This starts on page 95 and continues to page 101 in the original 1977 edition (interrupted by several pages of photos).
So it seems like he's referring to two separate incidents. It would make sense if it's from "Three Missing Links" for me to not be as familiar with the scene, as that short was on a list of films that weren't shown on TV in Chicago for a number of years, and my Ultimate Collection DVD set is currently MIA.