I had the exact same problem when I bought LED tails for my '10... instead of fighting with the seller to get the correct plug on the lights (and yours sounds exactly like mine, it was a really flat plug) I just cut the plug off the lights, then cut the stock plugs off the truck (leaving enough wire on the plugs to re-attach if needed). I then soldered the wires from the lights to the wires from the truck and they worked fine.
I know some people freak at cutting wires, but it doesn't worry me... thats why they make solder and heat shrink tubing. :smileup: