Edited: another fuel/temp gauge thread, but turns out the harness is melted together

I understand that the cluster is powered by G5 which is a dark blue wire that connects to the printed circuit board and powers the gauges and warning lights:
So if the brake warning light works, then there is some power available.
Since the fuel sender moves, there must be some power flowing through the IVR to the gage and the sender back to ground.

Yes there should be a ground connector that clips to the sender and fuel line.

Here's how the gages and senders work.
Thermal-Electric Gauges (Session 227) 1966 Master Technician's Service Conference 10

The filmstrip that goes with that