Vivat least vaguest.
Join Date: May 2016
The switch has three wires. One of the fat ones goes to the fuel pump, the other fat one goes to a positive voltage supply. In normal operation these two are connected. When the switch is tripped, the circuit is disconnected.
The third wire (the skinny one) is almost certainly a status indicator. It's the one which is causing your faulty signal. I would presume it normally sends a 12V signal back to the body computer, and if the switch is tripped, no voltage at all.
This switch is on the cabin wiring harness, not the dash or engine harnesses. So there are several interconnects where you might have a problem with corrosion or weak contacts.