Paulace, I have the schematic for Hot Shot, not Big Shot, but that circuit appears to be the same in both machine versions. The circled switch belongs in the B relay (pop bumper relay). The circuit basically just changes the scoring of the pop bumper between 3-ball and 5-ball rules.

I'm trying to follow this thread also. When I rescued my Hot Shot a few years ago from the basement of an old house being renovated by a real estate guy, I struggled with getting the bonus count on the machine to work properly. Another pinhead and myself worked on it over a few days before we finally got it working properly. I don't think it was ever clear to me how the entire bonus scoring process worked as a whole, but my machine problems ended up being solved with some very precise adjustment of the I & J relays (areas 3C and 3D on the schematic) , which I'm sure I adjusted at least 3-4 times each. Along the way, a lot of other components got cleaned, checked, and adjusted