I think I know how you could power it in all its glory. Im a dirt bike guy before a motorized bicycle guy. Some older dirt bikes only had 6v for lights , same volts as the white wire to power lights with these engines.
With a dirt bike all you have to do is get a 12v regulator/rectifier and a small 12v battery. You run the 6v line from the stator to the reg/rec then reg/rec to the battery. This trickle charges the battery from the 6v engine line and allows you to run 12v lights from the battery. Ive seen this done lots of times when people restore old dirt bikes but want to run newer , brighter 12v lights.
I bet it would also work with these engines.
A reg/rec like this :
And a battery like this :
Super Mini Moto Pocket Bike 12 Volt Battery Parts 49cc: eBay Motors (item 170269544430 end time Sep-26-10 02:01:22 PDT)
Then you could run the 55watt H3 bulb that comes with that light and any other 12v stuff. You could hide the battery and reg/rec under your seat.