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.
@Capt_Jack_our_Basenji:
What camera do you use if you dont mind my asking.
The first two pictures are taken with a Nikon Coolpix 5700 and the other two with a Sony Cybershot W80.
