Answer: The simple explanation is that the oil pressure sending unit is telling the warning light that the oil pressure is right on the verge of being too low. The reason that the light goes off when you put the car in neutral is because the engine RPMs increase just enough to raise the oil pressure past the threshold required to shut the warning light off.
Unless you want to risk ruining your engine it is imperative that you determine whether the oil pressure is actually too low. The only way to do this with any degree of certainty is to temporarily install an oil pressure gauge on the engine to see what the actual oil pressure is. If the oil pressure is in the normal range, then replacement of the sending unit will most likely solve your problem.
This brings up the question of “what is normal?” You don’t say which engine you have in your Camaro, if it is stock, or how many miles it has accumulated. For most GM engines of this era you only need about 10PSI at idle with the engine warm. I’ve seen many high mileage engines running with as little as 5PSI at idle with the engine warm. It should rise to a maximum of about 35PSI – 50PSI at 2500RPM or above. When the engine is cold, don’t be surprised to see readings above 60PSI until the engine warms up.
Most (but not all) GM engines of this era have hydraulic lifters, and if the oil pressure drops dangerously low, the lifters will not “pump up.” If you hear you lifters start clattering away this is a sure sign that the oil pressure is dangerously low, and you should turn off your engine