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it could be your oil pressure sending unit. mine did the saame thing and i replaced it and everything is all good now.

 

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you can find them at autozone, napa, Aand A, advanced auto parts has them too. It is located on the drivers side down by the oil pan. It should have a 3 prong connector to it. its called a oil pressure sender. it isn't hard to take out. it took me 30 minutes to do mine. email me if you have any more questions. I can send you pics of where it is on mine and what it looks like. the easiest way to do it is to go under the car with a wrench to do it.
camaro_demon@hotmail.com

 

It is located directly above the oil filter and it would probably me about half an hour to switch if both of my arms were broke. J/K it's an easy fix.

 

Have the same problem too. Will you have to drain the oil out first. Or can you just take it out and not worry? Also what color wires will be getting pluged into the sender? Have 85 Z28. Can't seem to locate them on the damn diagram. Had tpi now carb.

 

I don't have a schematic on hand, but you will have to drain your oil.