John,
Sounds to me like the gauge sensor circuit is grounding someplace on the cluster. Specifically, the lead from the tank sensor actually provides a ground via the tank sensor float. To troubleshoot I'd try the following:
1. Disconnect the tank ground either at the gauge or at the tank sensor (might be easiest)... if problem resolves, the sensor cicuit is grounded someplace it shouldn't be... So you'll know where to look.
2. If that doesn't work, try removing the gauge and either: insert thin insulation pads on the mounting points, or remove the chrome coating on the mounting points. I'm having to guess at how yours is set up, but I think it is very similar to my Skylark.
If you have a dealer shop manual, there should be a troubleshooting guide in the electrical section.
Hope this is of some help...
Cheers,
JMC
2.
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John Chapman
BCA 35894
1965 Skylark Convertible