2013 Chevy 1500 5.3 Anyone Tow with this?

Assuming the trailer has electric brakes........ you need a power source to turn the trailer brakes on, ie battery, that will turn the brakes on "IF" the trailer gets loose from the hitch. Along with a way to charge this battery while driving. As the battery will drain with taillight, brake and turn signal use. This is actually not a big deal. As MOST GM pickups have had this wiring available to the rear of the box as standard since the early to mid 90's! NOT positive, but sure seems like most of the pickups in the last decade or so, have a plug built into the rear bumper for the most part as std too!
Under the dash, is a plug and play harness for a controller, that "SHOULD" or maybe in the glove box. I've gotten one with my new 2000, 2005 and my used 2014 GM's. A cheap $50 controller, "IF" you don't have a 7 wire plug already, 2 to 3 hrs max, $100 you are set to go. Of course, assuming you have some experience installing or doing this kind of stuff with tools available. If not, then the cost goes up I hope obviously! 
The Curt timer depending upon the cost, could in reality be more costly. I have not looked up the cost etc to see how it might be vs the known hard wire a controller, plug on the rear etc.

Take info for what it is worth. Especially since a 1500 mile trek will be in my world of driving a 30 hr drive ave 50 mph of actual driving. I'm assuming you are driving as I do around 60, a 5 min or so break per hr.......meals somewhere in the meantime per trip......

Good Luck on this.

Marty