Well then, if the engine oil cooler is installed, I guess you're good to go. In '08, the tow package included the cooler, a full sized spare (so did any 4x4 option...), and a trailer wiring harness.
I believe my tongue weight to have been in the 259 to 300 lb. range. On my '16, I've yet to tow a trailer, but have a plug-in (to the class III hitch receiver a motorcycle carrier which the carrier weighs at least 70 lbs and the Vespa-like 150cc scooter weighs in around 275 lbs, I do use a secondary support--a strap from the roof rack to the edge of the carrier, as recommended by the carrier manufacturer. There is no problem with this weight on the back of the Patriot--I was considering a larger carrier to carry TWO scooters, but haven't found one that I liked, and haven't really had the need. The carrier is just to have to take the scooters to the shop as needed, altho it may be fun to take them on vacation...
Good luck with your trailer camping. I've been looking at a "tear-drop" trailer--there's an outfit in OR that creates kits in the 6, 8, and 10 ft lengths. Kits are reasonably inexpensive, can be assembled with a minimum of hand/power tools, and are less than 1,000 lbs empty. I was reminded that heavy camping items should go in the back of the Patriot, and fill the camper with bulky, light weight items.