Oil light on when is hot and when rpm is under 1000

The chance is good that the oil was replace with thin oil. If the car idles lower than it did before the service it can also be the cause and need to be adjusted to higher rpm. No immediate damage to the engine forseen but need to be rectified asp especially if the car is going to idle frequently or for extended periods.

you have low oil pressure when the oil warms up cam barring or crank shaft barring main barring you can try a thicker oil like 15/40

If you have the correct amount of good quality clean oil in the truck, use a mechanical gauge to check actual oil pressure. If all is well, replace sender unit.

check crankshaft sensor.

check oil pressure switch located on side of engine block. not sure what side on a neon.

Oil light pops on at low rpm because at a low rpm, your engine is not running fast enough to maintain full pressure. this is because either you have an oil leak, or defective oil pressure switch.

Have a reputable garage check the oil pressure with a manual oil pressure gauge. Very well may have worn internal parts, or weak oil pump. Thats the only way to know for sure.

could also be wrong type of oil but worst case is the big end bearings inside the engine have gotten to big to maintain oil pressure and as you guessed the oil pump could be worn out, i would try changing oil pump first.

Most likely the oil pressure switch may be damaged. This is a simple procedure. Change and observe the results

I had the same problem with my 2003 Lancer OZ. The oil level and pressure were ok. Car was fine with no light when starting. After 10 to 15 mins of driving it would come on when I was stopped. It would go away when I pressed accelerator. Try replacing the Oil Sending Unit. It's about $10 and easy to swap. That was my problem.