Try checking the ground wire to your tank. Probably a bad sending unit !

Older vehicles had brass floats on the senders, and if they developed a pinhole, leaked, and filled up somewhat with fuel, they no longer "floated" on the surface of the fuel, but instead, bobbed up and down in the fuel. If your tank was full, then they would bob up and down in the entire height of your tank, going from empty to full and back to empty without any rhyme or reason. I don't know if a 196X GM would have a brass float, but the 57 chevy sending unit had a brass float, and this problem would cause the same symptom as you described.