There is one situation where it is really important that the fuel pump relay is not bypassed: in case of an accident. And when it comes to making an insurance claim for your burnt out car... The function of the fuel pump relay is to turn the fuel pump off when the engine stops turning, like when in a major accident, to prevent dumping fuel on the accident scene. Engine rotation is simply sensed by monitoring the ignition coil for pulses (where the CB or ignition amp is connected to the coil). When you turn the switch, it will start the pump to prime the system and then stop because there are no ignition pulses.

Especially in the 80's there were major problems with the manufacturing process of these relays which were never resolved, because the failure mode is safe and is usually after a few years which means they can sell parts without worrying about a warranty claim. Especially the 740/760 had this problem, and the solution is simply to open the relay and resolder all the large connections. The manufacturing process problem is that the relay metal bits suck up heat, causing the solder to cool at a different rate than the rest of the circuit, causing the solder to crack and/or form dry joints. Using a soldering iron, one can apply the correct amount of heat to the local area.

These relays were used through to the mid 90's, when the ECU took over the function of switching the fuel pump on and off.

Check the fuel pressure damper immediately after the fuel pump, it may be stuck and would then require replacement. It is just a diaphrame with a spring, an additional function is to hold pressure when you turn the engine off to prevent vapour lock in the fuel system. Also check that the in-tank fuel pre-pump (if there was one in this model) is working and that the hose that goes into the fuel tank does not have a leak. If pressure behind the fuel pump is low, then the pump also becomes more noisy. A simple check is to see if the car still runs fine down to reserve. If the pre-pump is faulty, you will start having trouble (cutting out) at about 2/3 or 1/2 tank (the pump is a "pusher", not a "sucker").

Whatever you do, do not let the fuel pump suck air. The commutator is exposed to (and cooled by) fuel, adding air will start a fire.

Have fun.