From your illustration, there seems to be a ground wire (blk or blu) missing from one of the M terminal (where the blue wires from the lanyard and funky switch are connected.
Since the funky switch has a blue wire and the other wire connects to ground, this means the motor will only stop with the funky switch and not with the lanyard or with the ignition switch. Why the previous owner decided to do this is anybody's guess.
A remedy is to add another blue or black wire to the said M terminal and then connect it to ground. This will allow the lanyard and ignition switch to turn off the motor, as long as the funky switch is in open or off position. If you want to keep the funky switch, I recommend replace it with a spring loaded switch that always turns off when released.
