Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Welcome to JUST ANSWER small engines, let me try to help you !! I don't know it all, but maybe together we can get you a satisfactory answer!
I see question is still open, do you still want help? Rapid overheat can be many things, but I would remove the thermostat, and fill the housing with fluid and spin engine to see if the coolant pours out, which would show that water pump is good. If coolant is circulating, then leave the thermostat out, and test run to see if ti still heats up, if it does, you likely have a leaking head gasket, letting compression into the coolant, assuming that the radiator and fan are working. The engine does have stator(alternator) mounted under the flywheel and can be checked with a voltmeter. Output from the stator, with the regulator unplugged has to be at least 28 volts AC. The bed lift is an electric motor running a pump, so you have to have good voltage before the motor will lift the bed.