If it was the wiring on the sender....
I.e. the wiring in the gas tank....The problem would be constant, and just not when the car is in motion.
Also I think the problem would be of a different nature, moreso the sender reading either constant empty (no output), or being stuck at a fixed reading, regardless of the level of gas in the tank.
Chances are you have a bad ground somewhere. I would check the sender, using the VOM meter....
Now the connection could be loose anywhere between the sender and the gauge, inlcuding the acutal gauge.... To see if the sender is faulty or having the wiring problem, have someone drive the car, while you have the VOM connected to the sender, and see if the reading of resistance jumps around. If the sender output remains steady (with slight variation from incline and gas moving around in the tank) then the problem is on the gauge side. - The gauge could be failing, or have a loose connection at the cluster.
I'm thinking something is loose and causing an intermittent connection, most likely a ground screw that has somehow vibrated its way loose.
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