A PC power switch is a two wire momentary on switch. Wiring it in isn't the issue (it's two wires, and in this case direction doesn't matter).
It could conceivably work if you wired it to the "start" position (momentary) but you'd need to use an ohmmeter on the harness with one lead on the ground and then test the rest of the wires to see which one "closes" in the start position.
You could also check it against the vehicle's wiring diagram, but that's going to be model/maker specific.
Without the wiring diagram it's impossible to tell....
Are both switches in series with each other? If they are it'd be a simple matter of wiring from one side of the toggle switch and the other side of the engine start switch. If they aren't and you don't care if the toggle switch actually affects anything then you could wire to the two sides of the engine start switch which should be a momentary on switch.