etrailer sells your model of hitch here.
http://www.etrailer.com/Trailer-Hitch/Chevrolet/Suburban/2004/C15324.html?vehicleid=200414111
On that same page they recommend this wiring mount/adapter.
http://www.etrailer.com/Custom-Fit-Vehicle-Wiring/Chevrolet/Suburban/2004/HM40975.html?vehicleid=20041170970
It looks like the wiring harness will unplug from your current trailer plug and plug into the back of this which you can mount wherever it will fit. They even have a video (which I did not watch) that shows how they installed it onto a Silverado of the same generation as your Suburban. It should mount the same since back then the Suburban and Silverado had the same hitches and rear bumpers.