Notes on Wiring:
I bypassed the separate solenoid for the original B & S motor, and used the Honda solenoid on the starter motor.
When looking at the very useful diagrams that Mark has posted, distinguish between the Ignition Coil (connects to the spark plug) and the other "Coil" which is the separate Charging Coil (i.e. the Magneto).
In order to stop the motor from the key switch, rather than the throttle control, I "killed" the ignition coil (rather than kill the charging coil/magneto). This is what the throttle-controlled Stop Switch does also.
Assuming you have the same key switch - test your own terminals for continuity first, or risk a melt down!
A test probe on my key switch terminals show that there is continuity between the G (ground/black wire) and the M (magneto/blue wire on my original B&S) when the key is in the off position.
So the M terminal is the one to kill the ignition, and is also what kills the ignition when the seat switch (blue wire) is not engaged.
NOTE: although the terminal is marked M, ensure that you connect to the Ignition Coil, NOT the Magneto(Charging Coil)
