To simplify from the description & diagram, the two wires from the "Driver module" under the rear seat to the fuel pump - one power, one variable ground - either not functional to the pump is ONE failure mode.
The other failure mode is a bad fuel pump - wiring fault internally, or mechanically frozen.
So - If you go by the color codes & where the wires actually go, you can test for a continuous circuit right from the plug to the driver module under the rear seat. No continuity (ohm meter), either the wiring is damaged or the fuel pump is "fried".
If you have continuity, momentary application of 12v. power to those wires & the pump should run, if it doesn't it's "locked up" aka "frozen". and No - if it's locked up it won't work, so it won't pump anything...