1968 barracuda temp gauge and fuel level inop
I had the same problem with my 66 Barracuda. I searched around the electrical forums and found some great information. And, several very smart FABO members helped me get mine going!! I'm not sure of the difference between years but the 66 has a voltage regulator inside the gas gauge that drops the 12 volts from the battery down to 5 volts to operate the gas and temp gauges. In these old cars the regulator goes bad.
I replaced mine with a 7805 regulator from Radio Shack and now have a working gas gauge. There are several great threads that have great info. Here's one link.
http://www.forabodiesonly.com/mopar/showthread.php?t=292861&highlight=sending+unit