Engine Still Running Problems with 1989 5.0 Engine

I got my 1989 5.0 running again after a 2-3 year period of inactivity. It turns out that it had lost spark from just sitting. I found voltage at the coil and at the ignition module so I guessed that the module was bad, I replaced that and voila, spark. But it still wouldn't start so I put a fuel pressure gauge on it connected to the fuel rail test port. Zero pressure. So after messing around with it I finally jumped the fuel pump relay directly to B+ and got 40lbs of fuel pressure. Now it starts but runs like crap. It seems to be running excessively rich and has an idle that is very inconsistent running high then low then high again. Eventually it stalls. When throttle is applied it produces clouds of whiteish gray smoke form both banks reinforcing the over rich theory. I pulled a plug and it was black and sooty.

So now I am wondering, did jumping the relay as I did do something to the fuel delivery circuit so the engine control module is out of the loop? How does this engine determine fuel/air ratio and correct it? Is it by switching the fuel pump off and on to maintain a pre-set fuel pressure? I thought it would have a fuel pressure regulator. I am just learning the logic behind this cars engine management system so am still guessing a lot. Obviously I could use some advice.

Thanks,

Randy

Car is a 1989 Mustang 5.0 convertible in stock condition. Car has sat without driving for 2-3 years and recently I got it running again.
Good spark, fuel pressure reads approximately 40psi. Car idles rough and idle RPM hunts and goes up and down repeatedly before eventually stalling.
White/light gray exhaust smoke billows out from both cylinder banks and lots of it. Does not clean out even when warm. Pulled a spark plug and terribly
black and sooty indicating to me it is experiencing an excessively rich fuel condition. Same plug used to run a perfect tan color. I jumped the fuel pump
relay to get the fuel pump to work so it stays on constantly until power is disconnected.

What might be causing this engine to be running so rich? What devices control fuel/air ratio and what should I be checking? Fuel pressure reads around
40 PSI so fuel pressure regulator must be working, right? Does the throttle position sensor affect this condition and if so what ohm readings should I get from it?
Any other ideas? O2 sensor(s)? Car used to run ok before I parked it. Not great, but nothing like this. It seems to be gagging from way too much fuel.

Any ideas? Thanks.

Randy

Not sure I understand. So 40 lbs at idle is too high? What should the pressure be at idle? If I replace the fuel pressure regulator is there any advantage to buying an adjustable one? The engine is stock except for a cold air filter and I do not anticipate any mods. I pulled the vacuum hose on what I think is the regulator and no fuel came out. Does that mean it is still functioning correctly or not? What I located is on the right hand side of the engine at the rear of the fuel log. It is buried under lots of wire and wire connectors and under what might be an EGR valve or something which is located directly behind and bolted to the throttle body and intake manifold. Just identifying all the control items on this engine is a pita. It has a ton of crap that is unfamiliar to me. My 1993 Chevy K1500 truck is simple by comparison. It has TBI injection. Even my 1988 Ford 460 port injected engine is easier to understand than this Mustang is.