Remember, if the engine is off, it will shut the pump down for safety. You probably need to set up, and cycle the ignition to get pwr back.
I would ohm out the pump at the tank first, don't trust test lights, use a meter. But always remember Kirchoff's Law, if there is no current flow, you will read B+, or in this case, battery voltage. Or GND through the pump's motor. If there is no load, the pump motor windings won't have any resistance to the current flow, giving you screwy readings that look good, but aren't.
If you are convinced that the motor windings are good and there is good electrical connections, run 1 of each wire (1+ & 1-) to the conn running to the pump by the tank. Connect each separately to the appropriate connections. It WILL start pumping if that works.
You should be able to measure the motor resistance (which will read very low resistance, like 5 ohms or less most likely) from the fuel pump relay output to GND. If you measure some resistance, I doubt I would even jack up the car. Apply B+ to the motor side of the fuel pump relay (with it removed), it should run.
The relay needs to be turned on/off. See what does it. ECM/BCM? Key? Fuse?