That is a voltage regulator used on the stock AC bikes. Maybe the previous owner put that on when he removed the estart parts.
As to stator modification: Instead of fishing a new wire down the harness for your floated ground point, you could remove the yellow from it's location and move it. Solder it to the ground wire that you unhook from the ground lug. So the yellow wire is now "the other side of the circuit".
White will be the "top" of the windings and yellow will be the "bottom" of the windings. There is a voltage trimmer on the TrailTech RR so with the engine at moderate RPMs you should be able to adjust it for approx 13.5 to 14.5 VDC output. This is based on a battery that you've already charged before installing.
I use a Ballistic brand 8 cell Lithium ion battery. It is closer in size to the stock battery than the Shorai battery that most guys use. It has a higher cranking capacity.
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2011 EC250E
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