On19 July 2007 at 18:25:21 UK time, WMR Bill in Pennsylvania, USA, wrote:
"With my new Moss sending unit and rebuilt fuel gauge, my needle bounces from full to empty with the slightest movement of the car. When stopped it appears pretty accurate. "

The fuel gauge is not electrically damped, so the needle will wobble a little in harmony with sloshing of fuel in the tank. If the needle bounces around the ends of scale when it shouldn't, like a light switching on and off, it means you have an intermittent electrical connection somewhere. Start with the circuit diagram shown here:

Check for loose connections on the fuse, Green wire(s), and Green/Black wires including the bullet connector near the starter switch in the engine compartment.

The fuel tank, mounted in rubber straps, is originally grounded through the steel fuel line to the fuel pump. If the steel line has been re-connected with a rubber hose you may have lost the tank ground connection. This can be restored by adding a ground wire from one of the sender unit screws to a grounding point on the frame nearby.

To test the sender unit use an analog ohm meter (swinging needle type not digital). Disconnect the wire from the sender unit, connect an ohm meter from sender terminal to ground, set meter on 100 ohm scale, and shake the car. Depending on fuel level, the meter should read somewhere between 0 ohms (empty) and 70 ohms (full). When fuel sloshes and the sender float wobbles up and down the needle on the meter should waver gently in harmony with movement of the float. If meter needle movement is jerky or erratic, the sender unit has intermittent internal contact, needing to be rebuilt or replaced.

If the sender unit and fuse and wires are okay, you finally get down to a faulty fuel gauge. Then you look into the articles on Fuel Gauge Function and Fuel Gauge Calibration.