No idea what the wiring for the LML Star is like, but traditional two-stroke Vespas stopped the engine by grounding the coil with a momentary switch.
So the question is: is it wired like a modern bike, with the kill switch interrupting the power to the spark? OR like a vintage bike, where it grounds it with a momentary switch?
The nature of the switch (momentary vs on/off) might offer a clue.
I should have moved this to NSM to begin with. There's likely to be quite a bit more specific knowledge from the vintage guys. Hopefully OP will get a better answer.
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