My Brother has had 2. He trained the first one to hunt quail but the dog would run after coyotes if he saw them. Jacks think they are big dogs and will take on big dogs and coyotes. Both my brothers' Jacks have been attacked by Coyotes in his back yard and both have survived "fighting retreats". Jacks seem to be happy living in homes with no other dogs and our experience is they don't get along with other dogs. Jacks in our experience only have eyes for their male owner and concentrate on them. They're great and fast on rats.
We have 2 Jack Russells and both are great dogs, tough with lots of energy, but also super smart. They love physical exercise, but like mental exercise as much or more. Keep them engaged and training as much as possible and you will have a great dog. They will pick up about anything you are willing to teach them. Not an issue with them sticking as long as they are trained. We use Dogtra collars as part of the training and its really helped. The rough coat Jack comes from a hunting line and he has an amazing nose for tracking.
Never had issues with peeing in the house...in fact, both were super easy to house train.
Don’t own a JRT but something I have noticed is people often cross breeds to help with the less desirable traits. I have a heeler German Shepard cross and he has been the best damn dog I have had. Going on 16 and doesn’t have any of the bad habits heelers often have. I say all that to say maybe a jack cross would be a better option.
My doggie is a patterdale terrier/jrt cross.....smart fella and all issues have been resolved with appropriate consistent discipline..over time the issues went bye-bye. 9 months old now and very well mannered but has a hellfire side to him which can be controlled.