There are several switches for each level. One for full. Three for 3/4. Three for 1/2. Three for 1/4.
The bulbs have power on one side. They're looking for a ground through the transmitter to turn on. The end path for that ground is provided by the "Push" switch at the indicator.
It looks as if the "Empty" light will come on no matter the quantity of the tank.
If your tank is full, you can use the "Diode" function of a VOM (properly biased) to check your switches.
Pin "1' for the red lead. Pins 4, 3, 5, and 2 for the black lead. Of the lights with three switches.... each one cannot be checked individually, but you'll know of at least one that is working if your meter shows a voltage drop (usually .5 VDC).