Fuel Gauge Follow up question; Formula
 

I have finished the tank and sending unit and fuel pump replacement, all is good. Put about fifteen gallons in and put 100 miles on the Pontiac this week end, ran flawlessly. Getting new tires this week and replacing the bumpy riding 25 year old uniroyals (I kept the speed down this week end). All that is good.
My issue is the fuel gauge is still not registering despite my best efforts. Does not appear to be a fuse issue, I have power to the trunk that connects to the sending unit.
The gauge does not move or change position regardless of key position, seems to be dead well below the empty mark, like it is getting nothing in terms of power. I recall that a bad sending unit will cause it to pin EMPTY when the key is turned though it is not doing anything. At this point, I am inclined to think it is the gauge itself. Anyone chime in on this? I have checked the wiring to the top of the tank and the ground, it is all in tact.
What am I missing? Does not look too bad to get the bezel off but before I go to the trouble wanted to see if there was any way to test this? Can I send power back to the gauge from the trunk connection to determine if it is the gauge?
Thanks as always, appreciate all that has been shared from everyone.
Scott.

Why not pull the bezel and the gauge and swap in a test gauge. Pick up a cheap gauge from the parts store or even Tractor Supply.

If you want to work it then this is the detail; The float in the tank is high with a full tank and it drops as fuel is used. With a full tank the float is at the top and the resistance is low (or near 0 ohms) and the needle will point to F. As the float drops the resistance will increase and the needle will point to E.

So based on the above a short circuit = low resistance = high current flow = F
And an open circuit = high resistance = low (or no) current flow = E

So assuming the gauge is working then if you only disconnect the tan wire at the gauge the needle should point to E. Which means the tan wire is likely cut/abraded somewhere from the sending unit to your gauge.

Thanks 70COPO, that is what I was looking for, the physics explanation helps a ton. I will pull the bezel and proceed per your suggestions.
Appreciate it.