Not a pro by any means, but will take a stab here...
You're adding an external kill switch on console, so it's not built into the ignition switch correct?
If so,
Without the kill switch (as originally wired, and was working), you have wires on each of the M terminals on your ignition switch..
This shuts off the engine when you turn the key to off right? And it'll start up just fine too right?
Now, ADD one wire from kill switch to one M terminal on the ignition switch. (Don't remove existing wire, just add this one.)
Next, ADD the other wire from kill switch to the other M terminal on the ignition switch.. (Again, don't remove existing wire, just add this one...
With lanyard in place, should start and run, then turn off when key is off Yes?
Now..
Start engine, then pull lanyard...
Engine dies....
Really should be that simple if I understand what you're trying to do here...