How thick is the back wall of a Class A? For mounting TV?

You can drill a small(1/16) hole in an inconspicuous location on the rear wall and insert a length of metal coat hanger, or other stiff wire to see how thick the wall is. With most coaches with a fiberglass end cap you may have quite a bit of depth.
If you have enough depth then you need to see where your cross members are. The cross members could be steel which might complicate things somewhat.
If you have the depth and want to recess the TV then all you need to do is cut the opening and install a frame on the inside to secure the TV. Once the hole is cut, it might be easier to run the electrical wires and antenna coax.

Hi, I just googled "2008 Georgetown Brochure" and there's a pdf with pictures of the layers of construction on 2 inch thick walls. I also so there is a Georgetown forum and several other possible connections that may be of help.

Just pulled my paneling off the side walls in the rear bedroom on my 95 gulfstream. The studs on my particular unit are welded steel, but do not run horizontal or vertical, but diagonal vertically about every 24 inches..
I'd be sure to use a stud finder and trace out the wall with pencil before committing to a location.
I see there isn't much "to code" type of building going on in a lot of RVs, they all differ drastically.
a quick phone call to the manufacturer may help.

A stud finder will be your friend. I would want to know where the studs actually are. They made not be on 16 inch center. Jut my opinion.

John. That's the exact info I needed. Thank you so much.

Just some rambling on my part since I'm not there to help and see exactly what you got going on there.

First, don't use 2 inch screws. All you need do is measure the thickness of the wall where the door is to get a good idea of how thick your walls are. The better rigs will be thicker then the cheaper ones.

Second, you have studs in the back wall which are more then likely 16 inch centers. Now the question is are they horizontal or vertical I can not say. Sometimes you can see the stud showing on the outside skin when there is a morning dew on the rig.

Third the idea of screwing a board to the studs then the swing arm to the board is a good suggestion. That should be strong enough to hold your TV.

Forth, since you got a Class A I hope the studs would be welded steel or aluminum. If they are wood I would sell the rig and upgrade before you start to have future problems.

Do you have any idea how far studs are typically spaced in a Class A on the rear wall? Also would the studs most likely be wood or metal? Reason I ask is there are no seams in this part of the wall and no screws that I can see. Thanks.

Use a studfinder to identify the stud pattern, then mount a decorative piece of stained oak plywood with routered edges with multiple screws into the studs.

Mount your tv swing arm onto the plywood. Incorporate a couple of pieces of material with Velcro fastenings on the front to hold the TV against the plywood so that it is not going anywhere when it is tied down.

If that place on the wall will always be used for a TV from now on, then how about gluing a piece of plywood to the surface of the paneling?