Thanks for all the replies. I didn't get Jack at a traditional rescue I found him in the Ozarks, very rural Missouri, while on a road trip with some friends. He was a total mess and didn't look like he'd make it much longer so I decided to take him home to Boston.
Are there any methods to determine the breed of the dog if DNA testing wouldn't work? Having looked at a lot of pictures and video of the Entlebucher my feeling is Jack is somehow related to the line. He doesn't seem quite as muscular, his legs seem a little too long and I think he only has a single coat but besides that he matches the entlebucher really closely. The markings are exactly the same, the chest is the same, the tale is curled up, the shape of the face and the rest of the body are the same. The size is the same, Jack is 9 mos old and about 40/45 lbs. Really he looks like an entlebucher/appenzeller mix to me.
Also his behavior, like his markings, exactly match the descriptions given on the AKC website. He is the most intelligent dog I've interacted with, stubborn, independent but can't deal with being alone. He is amazing with kids and other dogs and has a really giant bark for a mid size dog. If he's not exercised/socialized he turns into a monster. He likes to leap and is really fast.
I'm going to upload some video of him and I'll post it here.