If this is your 62 pick up,I would pull the dash cluster out and check for a melted harness.It will be easy to trace with an Ohm meter (Battery Disconnected First !!!)to locate the short.The fuel gauge goes past full with an open circuit and to empty when the sender lead is grounded provided there is power to the other side of the gauge.
Wanted Good Woman:
Must be able to cook , clean , sew , tune engines and polish trucks. Must have old Stovebolt and garage. Please send picture of old Stovebolt and garage.
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