OK. I meant to check if there is vacuum at the fuel pressure regulator. If not you have a blocked vacuum port at the intake, just follow the line and use a can of fuel injector cleaner to clean it. Check the hose for cracks.
There is not too much to say, assuming that the car is in shape, no accidents with body damage near where the wire travel to the fuel pump. The fuel pump is activated by the ecm trough a relay (fuse block behind the passenger kick panel, marked N) that receives power from a 20 amp fuse (#6 on the same block as the relay). You can try to remove the relay and bypass it to check if the pressure stays even, just be careful not to short the ECM.
The attachment is a diagram and some more info. Just be very careful so you do not damage anything else. You could try a new relay, but what about if the problem is in wiring ? you will drive yourself crazy trying to find it. If you see that you can not guess just take it to as mechanic. Sorry to say that.