On my old rig, the rear engine stop switch is in the middle of the green "ground run" wire.
If that is also the case for your switch, try bypassing the switch with a cheater wire to a fresh grounding point. (Or clean up the grounding connection.)
If that fixes the problem, reintroduce the switch and connect to a new ground point to see if that will work also.
If so, problem fixed.
1995 38' CC Magna #5280 ****Sold 21 years of fun