The N sw. is 4 prong. Pins 3/4 should be for Engine starter
circuit. 1/2 are back up lamps.
The plug has a plastic saftey lock ring that has to be turned in order to unplug the harness at the sw.
On some models there is also a plug above the gas pedal in the cabin that you can get to. [ same harness coming from the tranny, through the floor]
If the car won't turn over in the cold [ like today !!! ] , hit the sw with a hair dryer and see if that melts the suspected ice formation.... if it does , just replace the sw......