Another possibility might be Rat Terrier. They do come in brindle, although that colour is out of favour. There is one in my neighbourhood that has a bit of a Basenji look to him, and his tail is very short.......not sure if it's natural or docked.
So pretty and unique; glad that you ended up getting him and hopefully he never has to find a new home again…moving and being displaced really can mess with a dog (or anyone for that matter)...hope you have many years of great fun and mischief.