He is getting to be an old man. Dogs do go through the same aging processes we do. As people age, some wind up with fecal continence problems, most do not. It would be logical that dogs would be the same. They are, after all, mammals just like us.
If it seems like he doesn't even know it's happening, perhaps Agile is right and his back is out. The nerves are obviously not transmitting the activity to the brain. As for action you can take to keep your floors clean? I'm not sure whether they make Doggie Depends. At least he's a Basenji and not, say, a St. Bernard.
Good luck and please let us know how it goes. (Bad choice of words??? Oh, well…you get the idea.)