Makes sense. So you are saying pull the relay and jump pins 3 and 5 which will provide 12V to the fuel pump and ignore the signal from the ECU.
One thing we don't know for sure is what year Land Cruiser @Francis K is driving. I think it is a 97. These circuits are different for earlier years.
A simple test would be to bypass the fuel pump resistor, shown on the schematic above. Toyota limits fuel pump speed based on engine need for fuel. Bypassing the resistor would provide 12V to the fuel pump all the time.
I didn't even know that someone made a bypass connector. Maybe it's more of...