ok you aren't understanding how this all works.
here's how it works.
the black/white wire is powered by the bank angle sensor relay. your fuel pump relay is fed with a black/white on the coil side, a black/white on the contact side, then a brown/black on the coil side (that goes to the ecu) and a brown which goes to the fuel pump.
the black/white is +12v DC
the brown/black is connected to ground by the ECU to turn the relay on
the brown is the power to the fuel pump
here's a quick way to check.
turn the key on, with the kill switch in the stop position you should have 0 Vdc on the black/white
when you turn the kill switch to run, you should have 12 Vdc on the black white
if you don't have this, then you need to investigate the engine stop circuit. it starts at the ignition fuse (white/black), goes to the kill switch, comes back on black to the engine stop relay, then leaves on a red/orange to the bank angle sensor where it's connected to ground. any issue in this circuit will prevent 12v dc on the black white. it's pretty easy to diagnose this issue by a lack of FI lamp on the dash when you toggle the kill switch (when you click it to run, the FI lamp will come on for a few seconds as the ECU powers up, the ecu is fed by the black/white)
if you have power at the black/white, then you need to see if the ECU is calling for the pump to prime.
unplug the relay, put your meter between the black/white and brown/black. when you set the kill switch to run it should show 12 Vdc for a second or two, then go back to 0 Vdc.
if you plug in the relay, you should be able to feel the relay click on for a couple seconds, then off again as you cycle the kill switch.
if you're so inclined you can also put your lead between the solid brown and battery negative and verify 12 Vdc for a few seconds during the prime cycle
if you have all this, then the issue is further down the line
check for 12v DC between the brown and the fuel pump body. there's a green wire that bonds the fuel pump housing to the chassis. measure there.
if you have 12v going in, then it's likely that your issue is either a dead pump or a failed connection in the bulkhead that crosses between the outside of the tank and the inside. you can check for 12v at the pump motor connector itself.
chances are if you go through all this, you'll find the issue.