The tank indicator light always receives +12V and only gets ground when the tank is low. If it comes on due to light switch rheostat operation it means it is getting another path to ground. You can disconnect the path to the tank to confirm the issue is local to the instrument and light switch. The other check is if it comes on solid or weak. If it is weak, then the best theory is that the light switch is shorting it to the rheostat voltage divider, but that also requires some short or conduction at the PCB/connector of the instruments between two separate circuits. If it is solid, then it is a short like Thomas suggested but still requires a leak at the PCB/connector.
In the voltage divider (not solid tank light) case the tank light would come on when the panel lights are the dimmest. Else the switch short theory seems better.
I still think there is a PCB/connector problem in both cases.