The tank fuel pump doesn't pump fuel to the engine, that's not its purpose. The tank pump is there to pass fuel from one side of the tank to the other, as there's a hump between the 2 halves to accommodate the propshaft.
A gauge issue is probably due to a wiring fault in the tank pump/level sensor module, which has been well documented over the years.
You can test the pump simply be measuring the current it's consuming. If the current is below 5 Amps, then the pump needs replacing. If it's consuming more than 5 Amps, then the pump is probably ok.