If you remove the stator from your bike (and it's an XR650R)what you would see looks a little like a waggon wheel with 12 spokes. On the stock unit two of the spokes have windings that are connected to a brown wire and a black wire with a red stripe, those two windings make the (AC) power for the ingnition and the black/red and the brown wire connect straight to the CDI box. In addition to the first 2 there are 4 other spokes with windings that provide power for everything else. These four windings are connected to a green wire and a white wire with a yellow stripe. On your bike these two wires bring AC power to the 2 yellow wires from the regulator/rectifier. The reg/rect converts the AC into 12 volts DC which comes out the black and red wires. The battery and all the lighting power for your bike comes from the black and red wires. The six remaining spokes on the stock stator have no windings at all. When they rewind your stator the coils added to 5 of the empty spokes become the second 125w power source and are connected to 2 white wires that are added to accomodate this. This is one of the ways you can tell if your XR has a rewound stator. A stock stator will have 4 wires comming out of the case (brn, blk/red, grn, wht/yel), a rewound stator will have 6 wires exiting the case (4 plus the 2 white wires).
Even though the stock AC regulator is still bolted to the frame, on most dual sport conversions (with a stock stator) it is not connected to anything.
I know I went on a bit but I hope I was able to make this clear.
Also, I don't know what part of California you live in but I'm in the Bay Area (Silicon Valley) and I'll help you out with your wireing if your local. I can also email you any schematics you might need for your XR, stator, or DSK. Just PM me and I'll set you up.