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.
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.
