To check the fuel gauge on most Smiths type systems, turn the ignition to ON and remove the wire (usually green with a black tracer) from the sender unit. This should cause the needle on the gauge to read empty. 

Now connect the wire to ground and check that this causes the needle to move to the full position. 

Most Smiths-type sending units (that are metal) ground through the tank itself. If the tank is new, the exterior paint may be preventing an adequate ground connection. 

If in doubt, run a separate ground wire to the chassis from one of the screws that secure the sender unit to the tank. 

If your Smiths type gauge has a needle that is bouncing, then you most likely have a failed Voltage Stabilizer. The Voltage Stabilizer is located on the back of the dashboard. Replace the stabilizer to resume your correctly operating gauge.

To check the fuel gauge on Jaeger Systems, you will pull the wire that goes to the sending unit. This should cause the gauge to read full. If you ground the wire, your gauge will read empty. 

If your gauge reads empty and pulling the sending unit wire from the gauge does not make it read full, then you have a poor ground connection to your dashboard. Please make sure  your gauge is grounded to the dashboard or that your dashboard is grounded correctly.

As a note, the Jaeger systems do not use a Voltage Stabilizer.