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.
That little guy is soooo adorable! I just love it when Bs 'wag' their tails…... love the markings on him-too funny the you-tube next to all that space stuff! Good luck with Hubble!
I'm always amazed how Basenjis sense when you're ill and use the healing technique of keeping close.
I had a very nasty fall once and was knocked unconscious - I came to to find the Basenjis positioned all round me lying as close to me as possible.
LOvely pictures again, Jess.