[VetteVet]

here is a bigger picture of the factory switch. Your switch is missing some wires and depending on which wires you have on it, it may short to ground. The purple wire is the starter solenoid wire and goes on the ST terminal. No other wire goes there.

The red wire is the power wire from the battery.
The brown wire is the accessory wire
The brown/white is the alternator wire to the external regulator for a gauge dash,not an idiot light dash. On those it goes to the alternator light. It goes with the brown wire not the purple.
The pink wire goes to the firewall block for the ignition coil.
The tan wire is for the brake warning and then to the dash cluster to the warning light
The green wire is from the temperature sender and goes to the dash cluster
The dashed purple wire is the same wire as the other purple and it goes to the neutral start switch for automatic transmission trucks.

There's no reason to do away with the brake warning wires because they are just grounding wires for the light in the dash cluster. Don't connect them to any hot wires on the key switch. The key switch grounds the tan and green wires when it is turned on as a check for the lights in the dash cluster . I will check the diagrams again just to be sure