As an electrical engineer for over 40 years, I want to provide a bit of clarification to what berts said about solenoids. All a solenoid consists of electrically is simply a coil of wire. It creates a magnetic field when, in this case, a DC current passes through it. The amount of current it draws is determined by the resistance of the coil, which is typically under 5 ohms for a PTO. A solenoid does not draw watts per se. It draws a specific current based on its resistance and the voltage applied. When you multiply the voltage across the solenoid by the current through the solenoid, you will know the wattage or energy being used. A solenoid may specify a wattage in its spec sheet, but that is only when the unit is operated at its rated voltage, and when it is cold. [as a side note, the resistance of a coil actually rises as its temperature rises, causing less current to be drawn]
A solenoid does not behave in such a way as to draw the same number of watts, regardless of the voltage applied. In other words, if you took a perfectly good 12V PTO clutch and connected it to a 12V battery, it will draw a certain amount of current(likely to be in the 3-4 amp range based on a coil resistance in the 3-4 ohm range). If you take that exact same PTO clutch and connect it to a 6V source, it does NOT draw twice the current. In fact, it will draw half the current. The power is also halved. Why? Because the resistance of the coil remains the same in both cases. Ohm's law still applies. Current=Volts/Resistance
Specific to your problem, I'd suggest using your ohmmeter and checking the circuit(with battery disconnected of course). Disconnect clutch and check its resistance first. If the value you measure is significantly below the 3-4 ohm level, then it would appear your PTO is hosed. If it's good, then I'd work my way back looking for short of some kind to ground.
I submit this with the deepest respect for berts and his extensive experience! Not trying to start a flame war, rather I just want to give Ohm's Law its due!
Keep us posted!