I was thinking the oil pressure sending unit also because I've heard the same thing but I looked at the wiring diagram in the Haynes manual the other day and the power goes to the relay, then the pump. The power also splits off before the relay (bypasses it) and goes to the sending unit then on to the pump.

I changed my fuel pump relay the other day and that didn't fix it. I tested the old one and the new one with the aid of a couple alligator clips, a 9 volt battery and my multimeter. They both tested good but I changed it anyway.

Right when I was about to hop under the car to change the fuel pump I decided to pull the upper part of the intake manifold off to test the fuel injectors (easier than changing the pump) and I found my problem.
Two injectors showed 12.2 ohms, two showed 12 ohms, one showed 11.9 ohms and one showed 4.6 (might have been 4.9) ohms.
I just installed some remanufactured Bosch fuel injectors from SouthBay Fuel Injectors yesterday and I'm going to go out there with the air compressor in a minute to make sure there aren't any puddles of gas on the engine that haven't dried yet then try to crank it with a fire extinguisher on standby just in case. I've got my fingers crossed.

 

Got it running good today after chasing down a couple vacuum leaks because of a massive suction noise and a few intake backfires.
The remanufactured injectors and correct timing worked wonders for the power that car puts down.
It'll light the tires up from a stop on dry clean (no sand) pavement without touching the brake. It will also power brake with ease. So I'm happy.