Hey, it all worked out in the end, Paul, which means the whole process was a pleasure.
I haven't seen the wiring diagram, but it sounds as if that other wire from the flywheel area was the alternator/generator output, so as expected, the previous tenant was applying 12 Volts or so to the kill wire whenever the engine was running. The world is full of people who don't know there is a difference between magneto ignition and Kettering ignition: cars need 12 Volts on their coils to run, so mower engines must also. I wonder how he thought it started, if it needed 12 Volts on its coil for the ignition? Oh well, as a rule of thumb, never expect previous tenants to have been logical.
I'll close this thread.