@Zip143 , On this particular scooter, turning ignition key ON will light up: headlamp, license-plate lamp, instrument lamp, taillight, and winkers if switch was flipped left/right.
1. Question about blue-section between battery-power and rectifier.
Is it plugged in? This is usually "turn-on" signal to RR or voltage-sense line for it to adjust output based upon charge state of battery
2. in its current wiring-configuration, does it turn on all those lights if ignition-switch was turned to ON (battery-charger not connected)
3. what is battery voltage with everything OFF?
4. what is battery voltage when you turn key to ON?
5. what is battery voltage when you push START button?