Nice diagrams ! .
? Is there a files place in this forum you can save them to and label what brand & model scooter they're for ? .
A Magneto is a simple alternating current producing device that uses permanent magnets instead of an energized rotor with slip rings .
All you needs do is : change the A/C current into D/C current via a full wave D/C bridge and some way to regulate the excess charge when the engine is sinning fast .
Zenier (? SP ?) diodes work well, they're a shunt but sometimes, like in vintage British Motocycles they go open circuit and allow unregulated current to invade the entire electrical system, why some older bikes have reputations for blowing the headlights out .
Older Honda Motos use the lead/acid battery to regulate the systems voltage, this is sort of like having a really BIG capacitor .
Lithium batteries don't do well in these simple charging systems that lack proper voltage regulation .
You scooter prolly has some minor fault you'll find in due time .