Bad of missing ground between the back of the engine and the firewall.
The secondary power ground is between the back of the intake manifold and the driver's side firewall. It is often missing or loose. It supplies ground for the alternator, A/C compressor clutch and other electrical accessories such as the gauges. The clue to a bad ground here is that the temp gauge goes up as you add electrical load such as heater, lights and A/C.
It's a ground issue, but it might be the one on the cluster. I changed my cluster lamps to LED's, and while I had it apart cleaned the ribbon cables and all the contacts. Now mine stays steady when I turn the lights on.
It is actually an anti-slosh module for the fuel gauge. Notice on the diagram that the voltage source and grounds have a common source. The voltage inputs are all tied together and the grounds are all tied together