We have a high energy terrier - not a JRT, but I still thought I'd share our camping experience with this dog.
We raised the dog from a puppy and crate trained her. This means that when we were not paying attention to her, she was in the crate - never alone by herself, but frequent bathroom/play breaks and high praise when done outside. This is not punishment, nor is it cruel. We didn't go camping until after she was crate trained - although this was mostly due to scheduling.
We did make the mistake of getting a pee pad - DW's idea which I objected to. Do not do this. Now our pup thinks that if she has a towel/rug in the crate, it is there to pee on.
I would not leave her loose in the house for extended periods as she is still into chewing stuff up - irregardless of the multitudes of stuff meant for her to chew on. However, she was recently left in an unlocked crate, and was found sleeping in it - door ajar. It's where she feels safe.
We bought a collapsible soft sided crate for camping, and as we like to sample local cuisine on our trips, she sometimes has to stay behind. We also leave the radio on for her, and she seems to be content to go to her crate when told to do so. If not, then we could not go to places such as the naval air museum at Pensacola, Snow Mountain at Stone Mountain, etc. We did take her to Sea World with us as they had a great kennel for a low rate so we could enjoy the park.
Of course we take her on our hikes, but she can't go canoeing. We keep her on a retractable lead on site - found at CW or loose in the screen tent when eating outside. She also goes running with either me or DW, so the advice given above to exhaust them is good. An excellent chew toy is a deer antler. You can get them at pet stores - although expensive, but they last long and chewing is good stress relief.
I love all my animals but I don't treat them like a human. They are used to a routine and they are happy to follow it. We allow her on the bed until we put our books down, which is her cue to jump down and go to her own bed.
I believe you can train your dog to behave as you see fit. I would not leave a young dog uncrated in a TT. I'm sure people do - just not going to happen in mine. I've replaced lots of interior trim in my home due to the pet habits of the previous owners.
Experience without good judgment is worthless; good judgment without experience is still good judgment!
2018 RAM 3500 Big Horn CTD
2018 Grand Design Reflection 303RLS