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.
Tilly is beautiful and that is a great picture. I do think the tri's are very beautiful. When were at the dog show Saturday there were two tri's. I told Jaycee to bad they were not little were I could put one in my pocket and we run away.
I do not know the name of the tri boy but he was the champion or soemthing like that.
I loved Mammoth Lakes! My B/W Nika was like that. Always looking for the spot to jump over the water. Did not like walking on wet grass. She'd tolerate a bath now and then as long as the water was nice and warm.