This pic shows the three separate wires going to the sending unit:

...the gray wire is the wire that supplies the fuel level signal to the fuel gauge

...the brown wire is the grounding wire for the whole sending unit...gauge and pump

...the black wire supplies the power to the intank pump

That white plastic cover that has come off its base illustrates one of the common problems that the older style sending units have: the wiring gets exposed to the elements; the signal gets lost; and things don't work like they should.

That brown wire with the female spade terminal that fits onto a male spade soldered onto the cover is where some serious problems can arise. That terminal IS the ground. If the ground is lost, the intank pump will not run, and that usually results in the motor not running as well.

Having that terminal connection open to the weather was not exactly the brightest idea. I've seen those terminals rusted away....GONE...

...which was basically why the car was towed in to the shop.