Not sure how much extra load you can put on these little batteries but I would think you could tap into the wiring for the main light from behind the front panel, usually just a half dozen screw's holding it in place. be sure not snag the steering column with any cables.
Isn't the magneto an integral part of the generating system?? Since the voltage varies considerably in these scoots be careful not to add L.E.D. lights that are sensitive to high voltage. Or add a voltage regulator right after the battery and before your lights.
Magneto or stator plate or an alternator all depends on age and model of the scoot..
To wire extra lights in I would go to the live wire in to the light switch fit a little junction box and connect a wire from the JB to a new switch. Then wire from switch to new lights and you should be ok. Just check though that you scoots earthing properly otherwise you will suffer the curse of the dreaded blown fuse.. again and gain and again.
Voltage regs can be obtained from Beedspeed in Lincoln they are good!! You can find contact details by putting Beedspeed in a search line of say Google.
I'd run a wire directly from the battery to a in line fuse, then to a voltage reg., then to a switch on the dash, then to the lights. That way you leave the original wireing alone and you shouldn't have any problems with the fuses.