He said it shuts off when the battery runs down totally, which is why I think that he should address that problem first, as the pto switch is draining his battery, and the fuel shutoff solenoid is likely shutting it down. I agree, pulling the kill wire to the coils would help narrow things down a bit, but I doubt that his coils [both] are the problem, as having both of them die at the same moment each time is very, very unlikely. Testing the charging circuit is extremely simple. I think he will find his trouble there. free and easy, that is always my next choice, instead of wasting money.