I have a 1996 mustang v6 no power to fuel pump. Bought used fuel pump relay still have np power. Safty switch is good. Unpluged fuel turned switch on and i have constant power of 9.52 volts plug in pump looses power. Need help

Check the cam timing/belt condition.

When you turn ignition key on ( not start ) does the checking light ,light ? Check fuse's for PCM , are they good ? Find a wiring diagram an check power an ground at PCM . Also hook up a scan tool an see if it will communicate with the PCM . That's how you check the PCM ! Also check the constant control relay module , these go bad an they have fuel pump relay , power hold relay , this powers up fuel injectors an ignition system !

There is a switch in the airflow meter that keeps the fuel pump relay closed as long as there is airflow. With the meter unplugged, the pump should not run except when the key is turned to start. It would seem to me that you have a wiring issue. Try jumping the fuel pump relay so the pump runs whenever the key is on. (Remove the relay and jump the pump wire to the accessory wire--see top left diagram.) This defeats the safety feature but will keep the pump running.

I would check the EEC relay and the fuel pump relay for power and ground signals first. Both circuits are controlled by the ignition key switch. The fuel pump should be powered for 3 seconds when you turn the key on.

When you turn the key on it will only energize the fuel pump relay for two seconds , or until you crank the engine over . The PCM - engine computer controls the fuel pump relay . Watch this video
Fuel Pump Electrical Circuits Description and Operation

start by checking the fuel pump fuse and relay. will the fuel pump run for a few seconds when you turn the key to the run position? If so you may need to replace the crank position sensor. When this goes bad the engine will turn over and start, but only run for a second or two then die like its out of gas.

If you do not hear the fuel pump coming on and the fuse and relay check out good then you will have to see if there is power going to the fuel pump. if power is present at the fuel pump plug then the fuel pump is bad

try the emrgency cut off switch located in the trunk behind the driverside tailight.

If the Pump relay under the hood is still good, the fuse under the hood and inside the vehicle are not blown then the pump is faulty, replace the pump. If you need clarification on where any of these fuses or relays, the location changes almost every year, are I recommend that you get the Haynes repair manual on your vehicle.

looking for the fuel pump relay switch

pull a wire and ground it via useing a screw driver at the end of the spark plug boot to check for spark / if their is no spark / ignition control module / there is also a crank shaft position sensor / located on the back side of the motor under the coil packs / pain to get to / also the nuetral safty switch / to check the neutral safty switch diconnect the big harnest at the neutral safty switch put a fuse tester to the yellow wire / have someone turn the key / with the tester grounded the light should come on / now we know the ignition switch has power going through it. if there is a no power at the yellow wire / bad ignition switch / does the car have a relay located at the top of the radiator core support (up by the radiator looking down drivers side)if it does not gm will install one for free / if there is / look for the purple wire coming out of the relay and Follow it down to the starter / reconnect the neutral safty swtch / touch the small S (the smallest screw) terminal on the starter soilenoid / have someone turn the key forward check the light / this will detemine if the relay is good / CAREFULL NOT to touch the big starter wire with the little one it will jump the starter / I HAVE THE SAME CAR / Hope this helps