Gas gauge not working. 1966 Barracuda

You can check the gages and the senders for major faults with no power on using the resistance setting on a multimeter.
Also you can check the wires for major faults, like grounding.
That' s where I would begin a diagnoses.
You can do a visual check of connections and conditions at the same time. Wiring diagram in the service manual will show where the connectons are made and the color and gage of the wires.
The Master Tech Service Conference has a good explanation of how the gages work.

Side note: The ammeter [labelled alternator on the gage] works completely differently, and is wired seperately. It shows when the battery is discharging (running stuff) or getting recharged. Both of its wires are hot at all times.