Here's how the system works. There are two sensors in the rear bumper, one on the left and one on the right. The sensors point to the lane next over. When the sensor detect objects in the lane, it send a signal to modules in the front doors. These modules then light up the little indicators.
What I think is actually going on is that the truck is constantly sensing the trailer. Even though the sensors are pointing towards the next lane over, the trailer may cut ever so slightly into the detection zone.
From the manual,
"The SBZA displays may remain on if a trailer is attached to the vehicle, or a bicycle or object is extending out to either side of the vehicle."
You can disable the system while you're towing through the little information console. As an alternative, you should be able to fit an actual towing mirror to your truck from a Silverado or a Sierra. They come with power, heat, and turn signals. You would no longer need to blind spot warning system since you now have an real blind spot mirror that you can view.
