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.
Fula Nzara of the Congo was sired by Fulaflyaway of the Congo and my dogs are related through him. Queen Juliana was a patron of our club - the Basenji Owners and Breeders Association. It was wonderful to see the pictures, thank you for posting them.