So as a follow-up, I got my VOM fixed with a new battery. Tested the volts to the motor while my wife pressed +/- 10 deg on the course while in AUTO mode on the control. I got intermittent 0 to 2 V, more times 0 than 2. Power to unit is 12V. Unless the conductivity of the wire from the control head to the motor is intermittent, I think the unit is done.
So it is off to find a new control head unless someone has any other ideas.
OK, i know this is an old post, but let me put something straight. The ST4000+ outputs pulses to the motor. A simple voltmeter will not give you correct reading on that, and you will probably see something around 2V.
Since I was just repairing a faulty control head I got for a couple of buck on ebay, I found a thing, which might be a design problem. If the brass studs are screwed in to hard to the instrument, the case will crack and water can ingress from the behind. This particular instrument got a couple of drops of salty water just next to some of the analogue circuitry (that is where the screw is), which is even more sensitive to stray currents caused by the water. I soaked the circuit board in distilled water, then in isopropyl alcohol, dried it, patched the solder mask on the circuit board and epoxy'd the crack on the case, and now I have a working instrument :-)
It is fairly easy to disassemble a ST4000+, worth checking for water ingress.