It could be bad connections going to the fuel pump. I have thought several times that I needed a new fuel pump with the same symptoms that you note. But so far every time I have managed to get the thing pumping. This is not real easy to check with a voltmeter.
Mine is 445 but the setup looks similar. You also have supply + return voltage in these wires for the fuel sender.
On mine when the switch is turned on the fuel pump is energized for about 4 seconds then is turned back off until it's cranked.
This complete assembly is expensive so hope you don't need it.
I am told that the actual fuel pumps rarely fail. Some gets replaced when the problem was actually the wiring.
It may also have a relay to turn the pump on.