I will draw you up a schematic shortly and post a link to the picture.... give me a few
The relay pictured and the numbers used are a standard 30A automotive relay you can pick up in the light section of any parts store.
The diode needs to placed in the direction such that it blocks electrical path going from the upfitter to the factory lights, install it backwards and the lights will only work when you flip your upfitter and it will also cause the factory back-up lights to illuminate. You can pick up a basic diode at radio shack for pennies, I recommend when you install the diode, do it close to the taillight and solder and heat shrink the connection for protection from the elements.
Your constant 12V can be picked up from the trailer plug harness, there should be a full time (any time the key is on, at least) 12V there you can use, and I recommend a fuse be placed between the constant 12V and the relay, just in case.
What you are doing is powering the lights from that constant 12V through the relay, all the back up lights and upfitter power is doing is picking up the coil inside the relay. That relay probably only draws tenths (0.16 or so) of an amp, so no worries of overloading the factory back up lights.
I hope this is clear and helps you out.