The neutral safety switch should just complete the 12v circuit from the purple wire to the ignition. So if the switch is not closed, you won't have power to your ignition switch, at least that's how the wiring diagram looks. On mine, since it is not driving yet, I just jumpered the two plug prong for the NS switch going into the console to complete the circuit so I could start the car.
So I think if you are getting continuity from the purple wire to ground then it is shorted out somewhere. Probably on the side where it goes to your NS switch since it only shows continuity when you jumper it.