I may be wrong, butI don't think that harness will not work on your expy, unless they changed things on 2010. This is what I needed to use.

Amazon.com: Hopkins Plug-In Simple 47185 Multitow 7:4 Adapter: Automotive

I just plugged the 4 pin into the plug, stripped and connected the blue brake wire and found a place to attach the ground.

Hopefully the one you got will work for you.

btw, it looks like you have the same issue with the transmission cooler as I do. The bracked to hold it is there, but no cooler.

Scott