Take out your small heat shrink tubing and place a couple centimeters of it on your wires coming from the switch. Heat shrink is important in this case because it will prevent your signal wires from shorting out on the chassis of the connector or from one to the other. Solder the wires on the 5VSB and PWR ENABLE Pins. (Again see Step 9 for reference) It doesn't matter which wire goes to which pin as long as we can short the pins together for a Power ON status and separate them for an OFF status. Melt your heat shrink around these connections by either bringing your soldering iron close (but not too close) to them or by using a Heat gun or Hair dryer.
The theory behind the switch is that the 5VSB and PWR ENABLE share a common GND connection within the Power Brick so all we need to do is supply 5V from the 5VSB pin to the PWR ENABLE pin and VIOLA! When the switch is closed the Brick's LED turns green and the 12V Supply is activated and when it's open the LED turns back to Orange and the 12V shuts down.