The bottom line on this is that dogs are pack animals and don't like to be alone. Unless they are tired or confined, puppies will amuse themselves in ways we are unlikely to approve of. Usually as they get older they outgrow this tendency and also get to know what actions will earn them disapproval. Unfortunately many Basenjis don't give a rat's patootie whether you approve or disapprove of their actions, which is likely why as adults they still seem inclined to cause you grief.
In my experience, if they don't have a lot of opportunity to "practice" the "bad" behaviour while they are young, they seem less likely to continue when they are older. In practice this would mean crating or otherwise confining them to an area where they can't get into trouble when you are unable to supervise. I also believe it is much easier to end up with a trustworthy older Basenji if you were home to supervise much of the time when they were young. Having the opportunity to correct unwanted behaviour is superior to just preventing it by confinement, as the dog actually has an opportunity to learn something. In these days of absentee owners, perhaps the best solution is something like doggie daycare if it is available to you.