The small gauge wire is for the ignition coil and the other two are for lighting and charging, respectively.
One and a half of the thicker gauge coils are wound to provide power to the headlight, tail light, and brake light systems. Turn signals and horn are run from the battery, which gets fed (through a half-wave rectifier) from the other half winding.
My goal is to wind all three in series and rectify the entire stator so that we'll be running on 12V DC. We'll need a new ignition coil as the old AC one will no longer be suitable. All lights will be converted to 12V LED.