@little_t I think @JENGOSMonkey hit the mark when he mentioned two issues: boredom and exercise. The best way, perhaps the only way, to ensure that your Basenji will not misbehave is to make sure that he gets enough exercise.
Walks are paramount! Walking is an instinctive bonding period for canines. Those they walk with are considered part of their pack. Their family. Utilize the time to introduce and reinforce training while you walk and you will also be claiming the alpha spot in the pack. Your dog will respect your relationship more because your guy will understand it better.
Walks aren't all that's needed though. Keep your dog engaged and attentive by providing a variety of outings (when your schedule allows). Not all dog owners are fans of trips to the dog park, but allowing your dog to form relationships with other dogs can help them to be healthy mentally. So can trips to local hiking spots. Or walks in new areas. Or time with you at a local outdoor event. I try to mix it up for my B. We will do repeats, but the repetition is random, so my girl never expects what we will being doing.
Meanwhile, if you are present when your dog becomes destructive, a firm "no" is typically quite effective. You do have to be present at the moment. Telling your dog "no" after the fact is only confusing for your boy. It has to be a "caught in the act" response for your pup to connect the action with your instruction. Otherwise, you really can only use prevention as a defense, but your dog might just resort to attacking a different target.
Exercise could very well solve all the problems.