Crazy Gas Gauge
The 66 has a voltage regulator INSIDE the gas gauge. It takes the 12 volts from the battery and reduces it to around 5 volts. My guess is Ma Mopar was still transitioning to a complete 12 volt system.
Anyhow, it's a crazy set up. The regulator looks t a set of points and opens and closes to reduce volts to run the gauge.
Oftentimes the regulator fails. The temperature gauge uses the same 5 volts so if the temperature gauge is working, the regulator is good.
Another thing that causes problems is not having a ground strap at the gas tank. It looks like this and provides a ground from the gas output tube on the sending unit to the fuel line.
You can also just add your own ground from the sending unit to chassis ground.
I'll post up some links that may help you narrow it down.