I think what Homepin was suggesting was put some paper between the pop bumper switch. If the pop bumper still fires with paper between the switch contacts we'll know it's an electrical problem somewhere and not just a sensitive pop bumper.
Go into the self test #5 (switch test). With ball(s) removed from the game does the test show any switches closed? With the target up, activate the spinner. Does the test show any switches closed now? More than one? (edit: Troubleshooting might be tough. Pinwiki says "NOTE: Multiple closed switches will NOT display anything other than the lowest numbered switch. This can be an issue with various switch matrix diode problems, as the switch displayed as closed may not be the switch with a problem. There is a special test rom available that will show ALL closed switches in a sequence similar to how Williams' machines did so")
Now drop the target and note any switches shown as closed. Activate spinner with target down. Same switches or different than with target up?
Pinwiki shows this for the switch matrix. If I'm reading it correctly #5 is the spin target, 13 is the lower right pop bumper, and 10 is the yellow drop target. 5 & 13 are in the same row on the switch matrix, 10 & 13 are in the same column. Not sure what that means but I'll keep digging. Here is some good reading: http://www.pinwiki.com/wiki/index.php?title=Bally/Stern#Switch_problems