Originally Posted by FlyWright
Great idea testing the leads on your panel mount voltmeter with a DVM. At least it'll tell you if it's the gage or the wiring that's the culprit.
Undersized wiring or resistance through old connectors can rob you of voltage. I have a 12V plug at my helm that well below battery voltage. It looks like it's original equipment from 1977. Replacing it is on my long to-do list.
What confuses people with test equipment but limited knowledge of electricity is that resistance in a circuit will cause a voltage drop but that drop is proportional to the load.
For example, you could have a severely corroded connection in the circuit to your 12 volt socket and read 12 volts with a DVM that puts almost no load on the circuit, but if you plug a spotlight in, the voltage could drop to thee or four volts (or less). The rest of the voltage is dropped across the resistance of the corroded connection.
Remember also, current flows in both the positive and the negative sides of the circuit so resistance in the negative side has the same effect.
If this "plug" (socket) worked fine originally, I would be checking the connections in the circuit, both positive and negative. It's more likely to be a corroded connection than the socket itself.