Our 2005 Ford Escape, V6, would so similar. Low Oil Pressure lite on after warm up, pulling into the garage. Engine runs fine, no noise, etc. We do have some oil leaks on the passenger side, par for the course with Fords.
Anyway, had the oil pressure sensor/switch replaced with Ford OEM and comes on a bit less, but still comes on. So, installed a manual (analog) gage where the switch went. Lowest oil pressure I have seen thus far is around 14 PSI in drive/foot on brake, about 600-650 RPM (on the car's gage). Per the garage, they want to sell me a new motor for $6K. Can't afford that. I added some 10W40 synthetic oil to top it off and they said not to do that as the oil ports in the pump are very small and the heavier oil won't flow thru there. With 6 quarts of oil in this car, I hardly think 1/3 of one quart will hurt.
Oddly enough, I have called the Ford Dealership, garages, etc. "what is the minimum oil pressure for this car to be considered "low" pressure. No one knows. One friend that races cars told me generally around less than 10 PSI. So with idle in the 600-700 range, 133K miles, it may come on as some wear to the car but 133K isn't high mileage these days.
So, have no idea. Oil is always clean, 3K mileage oil changes, 20W last time, will go back to 5W20 per the filler cap and see what happens. Someone said to run flush in it before the oil change but no shop will do that, so not sure if I should dump a can in the motor, and then run up for an oil change. Use to be the thing to do to clean out crap out of the motor. So, still at a loss. Keep driving I suppose until it poops out, and then would need a motor. Being 10 years old, I doubt I would want to spend $6K on a new motor, $3.5K on a used one with 1 year warranty.