That makes sense, the circuit would be closed under normal battery only power, and with the alternator turning, the power supply would be above 13v and the circuit opens. Assuming the white wire is the anti-start relay, if I were to use a generic ignition switch, I would have to wire it to the ignition relay terminal (hot in run AND start position), or I could just leave it unconnected and lose the functionality, but not lose starting ability.

As to the previous post, I am aware of the mechanical anti-restart setup on some trucks, but this is an electrical module. Not sure on the true vintage of my truck, the parts guy told me late 80's.