If the oil light comes on while the engine is running - it would mean there is something you needed to get fixed. If it only comes on when the motor has stalled - thats normal. The oil pressure drops to zero very soon after the engine stops; it doesnt even take a second.
Im sorry I cant help you much about where to look for damage to the engine wiring harness. I was able to do it in warm weather, and I had removed the motor (to replace the crankshaft seals); so I had the wiring harness totally out of the car. I would not have been able to fix that harness if it had been in the car. The melted sections would not have been reachable or easily visible.
Another thought:
Have you or the mechanics checked the fuel pressure? A blockage in the fuel filter or fuel lines causing low or fluctating fuel pressure could also cause your symptoms. There is a Schader valve on the fuel rail for this.
BUT you need to be able to check it while you are driving. That Schrader valve has the same threads as the hose fittings that are used for checking the pressure in the old R-12 air conditioning systems, and those hose fittings have the 'pin' for depressing the stem of the Schrader valve. (Its similar to the valve stem for putting air in the tires of the car). When I checked my fuel pressure, I used my R-12 manifold/gauge set, connecting the low pressure hose to that Schrader valve. I brought the hose out at the back of the hood, with the gauge lying on the windshield, held down by the wiper arm. The hood still closed. Then I drove along on a highway, able to put my foot well down on the gas pedal. The pressure stayed very close to 49 psi, as it was supposed to. If that pressure drops more than 20% it could mean you have a partially clogged fuel filter - blocked by ice crystals if its below freezing.
You could also try putting a can of 'dry gas' or a similar product into the fuel tank. That would let you know if you had a blockage due to ice in the fuel system.
I dont know if Neons shut the motor down when the oil pressure drops far enough for the light to come on. Some cars used to do that a few years ago; and now a lot of the the newer ones dont. Because if you lose oil pressure in the middle of the G.Washington Bridge or in the Holland tunnel; for safetys sake you want that motor to keep running till your family is in a safer spot.