the high beams for each headlight get power straight from the stock plug.
the HID's get power from the ballast, which is connected to the ignitor, which is powered by the stock plug.
the corners are powered from the stock plug.
the ignition for the eyes is the red/white and dotted power wire in the ECU box. their power comes from the relay which is hooked up to the engine bay battery terminal which is, in turn, grounded onto the passenger strut tower by one of the existing 3 bolts. the remote on is tapped into the passenger floorboard interior light.
this just hit me as i'm typing this up - my alpine headunit sometimes flashes just as the lights do when i first start up the car .. maybe my alternator is dying? i did have a pretty nice accident a year ago in which it could have been damaged.