An Equinox, like any other toad, requires the installation of a base plate that is typically mounted directly to the frame of the car that is used to connect the tow bar to. A lighting system that consists of wires to activate the tail, brake, turn signals, and emergency flashers of the toad from the towing vehicle (motor home). And, a braking (not breaking) device that activates the car's brakes when the motor home brakes are activated and that also has a break away device that will activate the car's brakes if the car should become disconnected from the motor home during travel.
I can't speak for the Equinox, but I imagine that it is much like our Terrain. The front fascia has to come off (which is much easier that you would think) and the base plate will replace the front horizontal steel bar that connects the two lateral frame pieces. The base plate will have two points that stick out to the front of the fascia for the tow bar to connect to.
The lighting system typically just consists of a four wire flat cable that has a connector on one end that is mounted to the front of the car that the umbilical cable from the motor home connects to. The flat cable is directed to the rear of the car and each wire is connected via a diode to the car's tail/brake/signal lights.
The brake (again, not break) system can be as simple as a box that sets in the front floor in front of the driver's seat and has an arm connected to the car's brake pedal..or it can be a little more elaborate system that is actually connected to the car's power brake system via a special vacuum pump...or it can be a part of the tow bar. It will also have a small cable connected to the back of the motor home to a connector on the front of the car. It is part of the braking system and upon disconnect of the car during travel, the cable will pull a pin from the connector on the front of the car allowing the car's brakes to be activated stopping the car....hopefully without coming into contact with other cars or stationary things.
Hope this helps
Ron