love2fixit,
I looked at a diagram of a '65 with gauges. The fuel gauge finds a common ground in the dash assembly with a whole bunch of other things...the temp sender and lots of the dash lights themselves.
I wonder if a dash light or some other device is shorted and powering the fuel gauge through its ground. I don't know if this would give you the goofy problems you are having, but it's a thought.
Is there some other item on the dash that doesn't work, maybe a light, or gauge. Does the problem change when you turn the headlights on?
Stuart
