Sooooo ..... I've done a bit more digging, and found a third version of how to flash a Sharp, that matches the description lordvader gave
here.
You solder the bridge on the bottom of the motherboard as normal. You solder the Sharp specific wire (the red line in the second picture
here). For the bridge on the top of the board you need to solder a wire to each side of the bridge, but don't make the bridge - if you solder the bridge on the top of the board the Xbox will not boot. The wires need to be long enough for the free ends to be accessible after the Xbox is temporarily reassembled for flashing. Apparently it is easier to use 30 gauge wire, and solder it into the vias adjacent to the two bridge points, shown in white in the picture below. Insulate the free ends of the two wires for the time being.

You then boot, fire up your flashing application, and twist the ends of the wires together just before flashing. Once flashing is over you power the Xbox down, untwist and insulate the wires, and reboot.