That is absolutely not a purebred JRT, IMO. No way.
A JRT mix, sure. Maybe some ACD in there, I'd agree.
Basenji is an interesting idea, and I see the look ... but only in the last picture. Camera angle, perhaps?
We call certain dogs here at the shelter AAD's ... All-American Dogs. Or, more specifically, WSD's ... Wyoming State Dogs. These are lab/border collie/aussie mixes. Perhaps your uncle's dog is a ATM ... Australian Terrier Mix.
"We give dogs the time we can spare, the space we can spare and the love we can spare. And in return, dogs give us their all. It's the best deal man has ever made" - M. Facklam
"We are raised to honor all the wrong explorers and discoverers - thieves planting flags, murderers carrying crosses. Let us at last praise the colonizers of dreams."- P.S. Beagle
"All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost. From the ashes a fire shall be woken, A light from the shadows shall spring; Renewed shall be blade that was broken, The crownless again shall be king." - J.R.R. Tolkien