silver,
Do you have a 12v or 6v electrical system (positive or negative ground)?
Speed is right - bad grounds are the usual culprits. The gauge cluster has to be grounded and, as Tab posted, the sender has to grounded. You could run temporary test ground wires from the cluster "cage" to ground and from a sender-unit screw to ground.
If you have a 12v system, it might not have been set up correctly with a (Runtz) voltage reducer (as mentioned by 4.3) and the gauge is ruined (usually, this is "all-or-nothing" - you would get no action from the gauge).
Since the gauge is sometimes indicating "Full", the gauge is most likely good.
One more thing to do before either giving up or removing the gauge cluster and gas tank sender for a bench test: run a new/test hot lead to the "In"/"Hot" post of the gauge.
If you do reach the point of buying a gauge, before you do, remove the cluster and sender and do a bench test (you will know that your grounds and power leads good). A bench test is a pain but you might as well do it if you are going to take the gauge out.
I bet fuel gauges (bad grounding or 12v burnout)and weak starters (insufficient ground cables)are the most common electrical problems experienced by people with 50+ year old trucks.
Good luck,
Tim