2 things are bouncing around in my mind.... here goes!
1. if i remember correctly the 600 engine uses a stator (alternator) behind the flywheel, on the inside edge of the flywheel are magnets that rotate around the stator as the engine is running and generates AC voltage.
its possible something is wrong with the magnets, but not very likely. Sometimes they can fall off/out of the flywheel, but you would more than likely know if they did.
2. Also, sometimes (i know this is true on some Riding Lawnmowers) they have Diodes in the wires that carry the AC voltage, diodes allow current to flow one way, but not the other. And if they go bad current will not flow through the wire.
im not 100% sure your mule has them, but i figured its worth putting out their incase someone else knows.