I need to setup a 2007 Chevy Tahoe for towing.

I have a question regarding the need of the brake relay on my 2007 Tahoe. What I found is the brake lights do not come on when the key is off on this vehicle and the brake pedal is pushed. The brake lights only come on when the ignition is on. I plan to test it when my wiring harness comes in. I am thinking I may not need to install the brake relay kit which I already bought and cut open the package. I would rather not cut into my wiring harness on my Tahoe if I don't have too.
Mike