Many automotive LED lights have full wave diode protection and resistors for 12v built into them these days, but you have to check. If it is not there, build it in. LEDs will work on AC when protected. I have used them on my street legal KTM which has an AC system. The same KTM produces more voltage as rpm goes up so it has a regulator, which is really just a 12v sink. Any more than 14.5volts get put to ground (so it runs cooler and last longer with more lights on!). The AC pulse is so fast you will not see it at anything faster than an idle.
So to run a 6v or 12v SLA powered light off the white wire, buy a full wave rectifier and a regulator (off any small dirtbike or cheap old snowmobile). The fullwave rectifier will have 2 wires in (white engine wire and ground) and 2 wires out (+ and -). Your motor is AC grounded so you have to have +and- wires to everything. To hard to disconnect the coil ground and have the ignition work.
The regulator is a little steel or aluminum can with a single wire out of it. Hook this to the white wire (AC side, before the rectifier) and bolt it to the frame or motor. It regulates the AC by limiting maximum voltage to the ideal 14.3 or so needed for Lead Acid Batteries. LiFe or other types will need some sort of battery manager system (BMS).
I run a very small SLA (sealed lead acid) battery on my KTM (in the airbox!) now and have an LED white light in the headlight reflector (along with the AC powered halogen bulb) so if I dump my bike on a dark rainy road, lights will continue to work if the engine stops. Everything but the headlight is DC now, so it will work off the battery. Rectifiers suck watts so I run the headlight on AC. I only have 40W to work a 35W headlight bulb.
Steve