Oil pressure problem...

First, I will say that your oil pressure is NOT actually dropping to 0. You would KNOW if it did drop because the engine would be clicking and knocking...and then overheating and eventually seizing. The real problem is the oil pressure sender. The sender on these model year stangs don't function like the senders on older Ford vehicles. It acts as a pressure switch. 0 - 7 PSI and the gauge reads 0 (or off) , 8 psi and above and the gauge reads right in the middle someplace (or on). Its either on... or off.. not any variable position. If the gauge fluctuates, then the sender is most likely bad. In your case, it's a bad sender. Look right around near the power steering pump bracket, that't where the sender resides.

I replaced mine 3 times and I still continue to have problems. The sender most likely gets oil in where the switch contacts inside causing a variable reading or none at all. Oil by the way is a non-conductor or just a very high insulator. The sender switch isn't made all that well.

I had the same problem and replaced the sender. It's like a $10 part and is a cinch to replace.
Seeing zero oil pressure gets my immediate attention, so I replaced the part right away and so far it hasn't failed again.

I can never seem to have a proper working sender. I replaced the stock one years ago because it kept jumping around to 0 and then other positions on the gauge. I replaced the sender and all was well. 2 years later the gauge starts flickering around and eventually I had oil just pissing out the top of the sender. Scuse me for that but it was literally dribbling out at a medium rate. So I replaced it again. ..it worked good for one year ...And now the gauge sits at the left side of "N" in "NORMAL". I thought maybe the gauge connection was going bad. I bypassed the sender and connected straight to ground... The gauge shot up to "M" in "NORMAL". Right where it should be. So the sender has screwed up AGAIN. I don't know what the deal with these senders is. I bought this last one at Ford.. can you believe that? crrrrazy

How long have you owned this stang? If you have owned it for quite awhile, then I would sugggest you start changing your oil on a regular basis. Oil that turns blackish quickly means there is a lot of garbage/sludge buildup inside the motor. If you just bought this or haven't had it very long, the previous owner probably didn't take very good care of it. I don't recommend flushing it as this may actually cause a leak that say... some sludge is plugging up. You may choose to do so if you feel there is excessive amounts. If you do, take note of any leaks you already have just in case. Change your oil on a shorter term if you decide not to flush. Preferably use the oil meant for high mileage engines.