Quoted from plovis:
I just had this exact problem on a Bally machine, turned out to be a bad opto board for the flipper button. You could try swapping the flipper button opto boards. Its an easy thing to do that doesn't really require any electrical knowledge, just a couple plugs and a couple screws on each side. See if the problem travels over to the other side. If thats the case its a pretty cheap and easy fix.
Does Stern use optos or leaf switches for the flipper buttons? Either way, OP, check for a stuck switch first before doing more complicated stuff. Go into switch test mode and see if that flipper button is closed.