totazman

Whenever any electrically powered device (lights, brakes, etc,) is turned on (used) the gas gauge needle dips lower and stays there until all other devices are turned off.

ejboyd5

This topic has been discussed ad nauseam. Do a search for more information, but the quick answer is that you must add a dedicated ground wire to the sending unit on the fuel tank.

CaptainEgg

Agree with ejboyd5

65GGvert

Here's a quote from John Z from his article:

Response: These are classic (and chronic) C1 symptoms that have been experienced and dealt with by many C1 owners. The basic flaw in the circuit design on C1’s is that the ground for the fuel tank sending unit is shared with all the rear lamps, at the single harness ground at the left rear of the trunk; if this ground isn’t perfectly clean and making good contact, every time the rear lamps are in use (especially the bright filaments for the brake lights/turn signals), it back-feeds the fuel sending unit ground wire and causes the fuel gauge needle to fluctuate in sync with the bright filaments. This can be cured by removing the fuel tank compartment cover and adding a dedicated ground wire from the sending unit to the frame; run the wire across the tank and down through the hole where the fuel feed pipe exits, crimp a ring terminal on the end, and secure it to a hole drilled in the frame with a zinc-plated self-tapping screw and star washer. This will permanently cure the “dancing needle” syndrome.

Basically, run a ground wire from a screw on the fuel sending unit on top of the tank to the frame and make sure it's a good connection. I found a very good connection point on the passenger side below the tank, but the essential part is ground the metal part of the sending unit where the screws hold it in.