I had a few more minutes to look at the wiring diagram, so let's see if we can finish ironing this one out.
First, a few things about what we've got. I didn't realize the stock connector had 4 wires, now it makes a bit more sense (for reference, your truck has wiring colors associated with the 2010 FSM I had, not the 2009, but the pin-outs are the same). Those 4 wires are:
Pin 1 = Gray - Signal from BCM to switch
Pin 2 = Pink - Ground wire for the stock LED illuminating the switch
Pin 3 = Black - Ground wire for switch
Pin 4 = Purple(Violet) - Power wire from tail-lamp circuit that controls most dash illumination (comes on when your tail-lights are on)
This means the purple and pink wires are only used to power the LED that back-lights the stock switch. So, assuming you want the lower light to illuminate with the rest of your dash lights, they are perfect to match up to pins 6 and 7 on the new switch. It shouldn't matter which to which, but following convention on the switch diagram that would be purple wire to pin 6 and pink wire to pin 7.
Now, the cargo lamp switch in stock form only uses the gray and black wires. Moral of the story, when the switch closes they are connected allowing the signal on the gray wire to be grounded. When the gray wire is grounded the BCM thinks the switch is on and enables the cargo lamp.
The best way to give the new switch stock functionality will be to use the diagram inov8 posted (nice work, by the way). To do this, take the 12V constant that you have been using and attach it to pin 8 on the new switch. The gray wire will go to pin 3 on the new switch, but a diode must first be installed in-line to prevent current feeding back into the BCM. Something like this
should suffice and will probably be in stock at your local RadioShack. You'll need to make sure the diode is facing the correct way or it'll have the opposite effect.
Finally, the black wire from the stock switch is a body ground, and should be perfect for the ground on pin 2 of the new switch. If that's all installed correctly, it should work just like the stock switch (while looking much better of course).
To note, simply running a wire to the stock relay will not work in the way Dan mentioned. The relay has a 12V power source from the battery already, it needs a ground to complete it's circuit (which the BCM provides when it needs to switch the lamp on). You could use the switch to create this ground in a similar way to what's above. This would involve splicing into the pink wire from the relay (without severing it) and running that wire into pin 2 of the new switch. Then I'd use the black wire from the stock switch to ground pin 8 on the new switch, leaving pin 3 open. This wire should have enough power to adequately power the light on the switch.
The second configuration should have a similar result, and maintain a mostly stock functionality (still comes on with open door, etc.). The only thing I don't think this will allow you to do is manually turn the light off when it's on from an open door (in stock form if the switch is turned on then off the lamp turns off no matter what state it is in).
That's what I'd do anyway. Hope this helps!