1968 barracuda temp gauge and fuel level inop

You may also want to check your ignition switch, they tend to go bad or at least open up causing the fuel gauge regulator not to get 12 volts while the engine is running. You can possibly fix it easily by taking it apart and soaking it in WD-40 so the contacts make connection to ign1 and ign2.

As mentioned above, the problem could also be the in dash regulator (likely), the sending unit in the gas tank, the ground strap at the sending unit, the wiring from the tank up to the gauge or lastly and most unlikely the gauge itself.