Water in the oil

If your oil is full, it's most likely electrical. If it's not electrical, then it's most likely something like a crack in the pickup tube, sucking air if I had to guess.

I have to ask if you are sure the oil pressure drops first, or the engine stops first. The engine would stop if the oil pressure dropped below 5psi but only because the fuel pump would shut off. And it should start back up if that were the reason.
If something such as a relay or the ignition module is getting hot and killing the engine, it might have to cool down before it restarts. And the engine would stop then the oil pressure would drop to zero.

If I were you I would put an oil pressure gauge in place of the factory pressure sending unit, these can fail sometime when hot and cause false reading at the gauge, of the pressure seems ok replace the sender, oil viscosity can affect pressure readings but not to that extent, also check the simple things like your oil levels as these are commonly overlooked

something is strange here thats for sure ,firstly take thermostat out and put it in a saucepan of water and boil it to see if opens .,check the oil light switch and pull the rubber boot cover back to see if any oil is behind it ??.-You are buying trouble with a car with such a high mileage on it ,never buy anything with more than 50,000 miles or you are just buying someones rubbish

oil pump is faulty or worn crank and or rod bearings
A plugged collant gallery may cause this problem too

I assume from the year it has high mileage. With mileage comes wear in these engine's bearings allowing oil pressure to drop because of the excess clearance between cam and bearings, also the crank and bearings. When the engine is hot and idling the oil is thinner and goes by the bearings quicker. If you have good oil pressure while driving, I'd leave it alone, maybe use a thicker oil or some lucas additive. My 89 does the same thing sometimes in the summer, but don't remember it doing it this summer. I use Mobil-1 and an AC Delco filter.

You better put a manual gauge on your engine and make sure you have oil pressure. Could just be a faulty gauge or sending unit but I sure as heck would be checking it with a manual gauge.

you may have a faulty sending unit

I suggest you pass this one by - the oil pump probably is shot and you'll get a hefty repair bill on top of the purchase price!

I'm guessing your engine is'nt making any tapping noise with the low oil press.
Your oil pressure sending unit is most likely the culprit.
Is your car smoking when the temp. goes up?
You engine could be air bound or thermostat could be opening too late (might need new one).
PLEASE DO NOT OPEN THE RADIATOR CAP WITH A HOT ENGINE.