Depending on what their shop rate is, it might not be outlandish, but still seems a little high. Here's what I can tell you for comparison:
The last car (before the Buick) I set up as a toad was a Honda Accord coupe. I initially was going to do it all myself, to include Blue Ox baseplate and tail light wiring kit and Roadmaster Even Brake (a "box" system similar to your Patriot II). I started in on the baseplate install, following the instructions, but soon lost confidence in my ability to successfully remove the fascia and complete the install. I decided to take it to the local body shop I use. They had never done one before, but I talked to the owner and showed him the Blue Ox instructions and he decided he could do it. I ended up having him do the baseplate and the taillight wiring. (I did the wiring for the brake system myself) I believe the total was around $300 (at $55/hr).
When I did the baseplate on the Buick, I probably spent about 5 hours on it. If I were to do it again, I think I could do it in around 3. I haven't done my tail lights yet, but I don't see that taking any more than a couple of hours (with the help of a friend). When I did the brake system last time, I think I spent no more than about 2 hrs. If the Patriot is anything like the Even Brake, the only thing you have to do is wire in the brake controller and the emergency breakaway system.
So I would say it should take no more than 10 man-hours of labor.
Edit: OK, I looked at the Patriot II instructions and it is actually substantially simpler to install than my Even Brake was. There is no controller that you have to hardwire into your toad, you just have to mount the breakaway switch. I would see how much the dealer wants to just install the baseplate and taillight wiring.