Fuel pump not running - 1983 Nissan 280ZX

let me teach you fuel pumps , gasoline
some cars run the pump for 3 seconds key on. or running.
other only allow the pump to run cranked or running,
toss a coin , or read the service manual that will answer this..
first check fuses. not relays.
then check for 12 vdc at the pump cranked,
The ECU runs the relay and the pump, the ECU decides to run the pump or not.
A shop uses this thing called a voltmeter, DMM to measure voltage at the 2 pump pins cranked over.
and work from there, if voltage is good then pump runs and what is next FUEL PRESSURE. is next, and a bad fuel filter kills that.
or bad FPR..

The fuel pump only runs when the engine is being cranked or of course is running, it is shut off after about 1 second in the run only position.

If you can't hear your fuel pump priming then either, the pump needs replacing or the relay. If you replace the relay and you still don't hear the pump prime then it's the fuel pump.

the operation of most fuel pumps is controlled by the fuel pressure regulator
when the fuel pump gets to set pressure , the pump is switched of by the ECM at the relay level
maybe nothing wrong with your system just the system working as designed
if you have pressure in the fuel manifold when you turn the ignition on then the pump will not run but will if there is a fuel leak somewhere and the pressure drops off

When you say the fuel pump relay is good did you test for power to the relay circuit ?

Gauge fuse runs a fuel module that is installed to correct vapor lock. This module is what is running the pump. This module, called the hot fuel module is mounted on the passenger side behind the dash above the blower motor.

Hi! The fuel pump is designed to run continuously as long as the ECM receives data that the engine is running. Excess fuel is passed back to the fuel tank.

The fuel pump is also designed to power up for 2-5 seconds when the ignition is turned to "RUN" to pressurize the fuel rail.

If your fuel pump runs continuously when the car is turned off, it may be a "stuck" fuel pump relay.

wrong fuel pump? wires crossed, fuel pump should run when car is on, this is what keeps it running, maybe fuel pump is louder than original and you notice it more. Check your fuel filter. Get a tune up........

Check the fuel pressure at the fuel rail if 30 psi is not present it may be a bad fuel pump or fuel pressure regulator.

Some GM products also incorporate the oil sender switch into that circuit for fuel pump, so that in case of an accident, engine shuts off, oil pressure drops, in turn, shuts off power to fuel pump. May be worth a look at what your getting for oil pressure, as well as checking switch/sender.