There was some confusion in calling it a neutral [safety] switch, which is usually on an auto transmission. The switch in question here is called a Clutch Pedal Position switch, which is actually two switches in one. One is as a safety for the starter circuit, requiring the clutch pedal to be depressed to start the engine. The second is a cruise control cutoff, where pressing the clutch pedal disengages cruise.
If the desire is to jump the starter safety part, the wires are the purple/white and the purple that is next to it in the connector (directly next to, not diagonally). If the connector has letter labels at the terminals, they would be terminals A & C (see pic below, looking into end of plug). BTW, this is for a 2000. @Kingjuliantaylor didn't give the year of his S10 but the plug is probably the same