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.
Buddy is not an under cover dog he'll start at the top of the bed, get his nose just under them and push them back to the foot of the bed bunched up then lay against it.
Is it possible for a house living B to be any thing but a "hamburglar"? Mine doesn't beg but I can't leave anything for even a millisecond. Laying on the couch, sweet as can be, next thing ya know, spaghetti on the floor!! D_m stealthy b_t_ds!! Still gotta love their intelligence….despite recent reports! đŸ™‚