Those two gauges have different power sources, so the only common link here is "ground", as was mentioned. The gauge cluster needs to be firmly screwed into the dash frame, and you might want to check that the ground strap for your gas gauge sending unit is solidly in place. On the pick-up tube of the sending unit, there will be a steel strap that runs over to your solid fuel line. That is where the sending unit gets it's ground.
Mike