Very nice scoot Panamesc!
Don't worry about the switch.
The "electric start" is instead the horn switch. It's the spagghetti nightmare.
Nice shocks you have. You say they are mini ones. I guess they are from the old generation Mini (the real one). Have you got the part number
I can help with your wiring. I guess your lammy was from Barcelona, as it has the "PAul Ricard" sticker on the horncasting.
My lynx is also a points machine and never had any problem. Only 2 wires came from stator, green (spark) and red (to regulator), from then on the spagghetti nightmare came to life...
Maybe I can help with this wiring diagram with indicators
1:.- Sooo here's the theorically wiring loom for you. you can if you wish keep the electronic ignition or revert to points, as the live cable is only one
http://img529.imageshack.us/i/lince12vacelectronic.jpg/


2.- Battery lince, more complicated with indicators, too
http://img24.imageshack.us/i/linceintermintentes.jpg/


3.- Back to basics lambretta, no indicators, no battery
http://img24.imageshack.us/i/lincesin2.jpg/


Bon courage!
Cheers from Spain
Donlambretto