Magnum Neutral Safety Switch, effect idle? and wiring?

I don't know why it would affect the vehicle running once you get it started. Could be the switch, connections, harness, something in the trans/ linkage, I don't know whether it's integrated into the controller.
Just found this from Dodge "NSS is used to determine idle speed (varying with gear selection), fuel injector pulse width, ignition timing advance and vehicle speed control operation."