2010 Tohatsu 4 stroke 20 hp. Has remote controls. Does the wiring for the power tilit and trim go through the tilt AND starter solenoids? I have an intermittant start from key problem. I have 12 volts to the starter solenoid right lug. Starter works when I jump the solenoid or when I pull start it a couple times. At the same time it developed a non working power trim and tilt motor. I found a spot where the mice chewed thrpough the insulation and thw wire was grounding out to the switch on the cowl. I noticed a whiteish looking burn mark on the trim and tilt solenoid which looks cleanable. It has a new battery.