We have a 2012 283ts, with just the standard base two tone with graphics. I believe your gts is the upgrade with the full body paint. I think (not 100% sure) the paint is done by an outside vendor, not in-house at Forrest River, so getting the exact "color name" is going to be hard.
Since yours is an older unit you might have better luck taking your rig to an automotive paint supply shop where they can probably "read" your paint and possibly match the color.
If your just looking for caulk to re-do the seams, check the Dicor brand. It's pretty much the stuff everyone uses, and although I use the white on mine, I do believe it comes in several colors. Going to be nearly impossible to get caulk in the exact color match for your paint.