It should plug in by the bumper, but be careful. If it's too short you can pull wires when you turn. I would add a trailer plug in the bed, it's easy to do and makes life way easier. Surprised the truck with tow package didn't come with it already installed. I bet it's wired for it, just have to add the plug itself. The bumper plug SHOULD be good enough to go pick it up then decide what you want to do.
2006 Chevrolet Silverado 2500HD CCSB Duramax/Allison
2012 Puma Unleashed 356QLB FWTH