Ok. I'll try. What you are calling a CDI I think is really the Light Module. The CDI is not connected to the lights at all. The Stator is.
Start w/ the S8 4T. There is a light module that I have no idea what it does because I never needed to know. I assume it is a rectifier but that don't matter.
To make your headlights come on w/ the engine you MUST have all leds, and electronic flasher relays installed first. The power, from the key switch can be extended to the HIGH BEAM BULB ONLY. Unplug everything else that connects to the bulbs except the ONE green wire, and add the new power from the key switch. Add yourself a 5 amp in line fuse, and you are done. The stator, and key switch can both handle the 35 amp bulb pluss the 6-7 peak using the blinkers, and running lights. YOU MUST HAVE ALL LEDS PERIOD
S8 2t is exactly the same. Only difference is the stator is a DC stator. There are more complicated ways to do this by adding a rectifier to the output of the AC stator, and using a relay to interrupt the current or adding a second regulator to the DC stator but the key switch is easiest, and will work fine.
Otherwise clean the headlight switches w/ PB Blaster (NOT CONTACT CLEANER) and replace the Light Control module in a 4t, or the stator in a 2t, and live with it.
CHEAP CHINA SCOOTERS! Don't get amped up over them. If it breaks your stones to deal with then you should have bought a Piaggio!
But I... You don't' understand I... They shouldn't be like...
No buts, I do understand. They are like... cheap.