1978 KE100 Not Charging Battery
 

I have a 1978 KE100-A7 that has quit charging. I've never seen anything like what it is doing. First,it is a 6 volt system, it does not have a regulator, only a small rectifier. It has a magneto style charging system with 3 seperate coils; one for lights, one for charging, and one for exciting. I have checked all the wiring and charged and tested the battery.
So here is the wierd part. If I attach the ground lead of a multimeter to the battery ground or any other metal part of the bike, then hold the positive lead of the multimeter within a foot (without actually touching anything on the bike) of any part of the bike the meter reading starts bouncing all over, from 3 volts to 20-something volts (like there is an electrical field around the bike). If I touch the positive lead to the battery or the wires coming out of the stator I get the same readings, bouncing all over. After about 10 minutes of running, the turn signals and tail light quit working because the battery voltage is falling.
I have been working on bikes for years, but I have never seen a charging system without a regulator, so I'm lost on how this system even works. I just don't know where to even start. If I could just understand how it works without a regulator I could probably figure out where the breakdown is. Any help would be greatly appreciated.