Perhaps there's a flaw in my thinking... what is the Amp rating of the switch that smoked?

Maybe you should hook the 'hot' side to the terminal that feeds only the ignition (the way I recommended would allow you to crank the car with the ignition off, which is not a bad option to have in my opinion).

I can't see that wiring it only to ign hot would make a difference, except the chance of overloading that circuit, which is the other reason I recommended straight from main hot.

From looks of push button starter switches available on the interweb, looks like the standard is 60amp. Keep in mind though, that the switch only kicks the solenoid, inside which is where the contacts are made that actually power the motor.

In any event, if your smoked switch is significantly less than 60amp, that'd be the place to start.

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-Matt I ♥ my ♂