EDIT: LOLOL Did not see your last post
Maybe an easier/ more understandable way to troubleshoot this would be a 12V test lamp
With a sender installed, clip the test lamp to the battery POS (or starter relay "big stud") Test that this works by stabbing the probe onto the engine block. Should light
Now stab the probe onto the sender terminal, with vehicle wire disconnected. Light should come on. Now go start engine and re-check---light should go off
If this all works, the trouble is somewhere in the wiring. Think of this stuff as and END TO END system
The path is ground-------through the sender-------out the sender terminal----------to the wire terminal---------------through sender wire to the bulkhead connector-----------into the interior---------to the cluster PC board connector---------through the pin to the traces---------to the light socket--------through socket to bulb----------through bulb----------back out socket back to board trace----------and board trace goes to a "key on" ignition power source on the board to light the lamp
This is all like a chain. One break anywhere will stop operation