Agree with the above, and to add some clarity (hope it's not redundant)...
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The red oil light on the dash is NOT an indicator of oil level or quantity (ie. what you measure with the dipstick). The red oil light on the dash is an indicator that the engine oil pressure is below a minimum allowable level.
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There is a pressure operated switch that detects oil pressure. The switch is typically located: If you open the hood and stand in front of the car as if you're checking the oil. Look at the oil filter housing, left (passenger) side of that, down low- there is an item screwed into the bottom area of the oil filter housing with a single wire attached to the end of it. That's the oil pressure switch.
As a side note, these cars typically have some "fudge" electronics built into the dash, such that even if low oil pressure is detected, the dash red light won't yell at you until the engine RPM is raised above some pre-chosen level, I think it's around 1500 to 1800 RPM. Then the red light comes on and typically a buzzer sounds, as well.
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Getting back to the main topic- oil pressure is probably the most critical engine parameter in terms of needing attention "right now" if it happens to become a problem. Thus we come back to the questions asked above:
How many miles on the car ?
When was the last oil change ?
Are you sure the correct oil is in the engine?
Any running problems recently, that could have resulted in diesel fuel contaminating the oil ? (that could cause the oil to become thin and lose pressure)
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Potential good news is that sometimes the oil pressure switch itself gets old and flakey, and the issue is caused by a defective switch and not an actual problem with engine oil pressure. Your description of the issue is perhaps the most frustrating, as it seems to be intermittent. Oil pressure issues are not something to take lightly. I would recommend as a test: (first, make sure the correct oil is in the engine and not diluted with a contaminant such as fuel) remove the oil pressure sender switch and install a mechanical oil pressure gauge there. Run the engine at idle and slightly above idle, make sure you have actual oil pressure. (Note that oil pressure varies with oil temperature; when first started, a cold engine will commonly have above 80PSI oil pressure at idle. When fully warm, the oil pressure at idle typically falls to 20 or less. Oil pressure rises with engine RPM. Specific numbers vary, but a fully warmed engine will typically have 40PSI or more at 2000 RPM. There are minimum acceptable specs in the service manual, sorry I don't have them handy right now. If the oil pressure checks out, replace the oil pressure sending switch. (you can get one from idparts.com, among others). They're not terribly expensive. I'm hoping you just have a flakey sending unit- it happens. Keep in mind- continuing to drive the car without diagnosis, if it does happen to be a real oil pressure problem, could end up with expensive engine damage.
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Best of luck- please do post back what you find.