Well on the diagram, go to the right to the engine. It would be the small wire coming from "Mag Kill" to the "Ignition Module", on most mowers, that wire usually is
on a circuit that puts it to ground to shut off the engine, unfortunately yours is a bit more complicated, and the brake actuator fulfills several functions, including
sending the kill wire to ground to shut it down. I was curious to see if you were shutting down because your mag was being grounded, or that the fuel solenoid was
being shut off, which would account for the engine running an extra second or so when the lever was moved in, as it takes a second or so to run out that last bit of fuel.
The neutral shifts on the levers obviously work, so it is just a matter of eliminating suspects, so a test light or voltmeter would be handy.
remove the keyswitch from the mower, look at the terminals you will see letters that should correspond with the letter on the diagram of the key switch.