We got our first basenji 23 years ago, a pet. I loved her dearly (I was 40 and had wanted one since second grade!).
I don't think she actually had separation anxiety, I called it 'Play with MEEEEE!' syndrome. I was home all day, as were our kids, and she just did things constantly that got our attention if we weren't paying attention to her. Some of the things were destructive.
When we were all gone, she went into her crate, and was no problem there, as there was no one home to pay attention to her.
When she was 2, we decided maybe another would help get her attention away from us.
It was the perfect solution, it took care of almost all her destructiveness. I guess she just needed someone, dog or human, to play with her. Sugar and Spicer!
I've said since then that she was the perfect 'first' basenji and taught us what we thought, not only how bad a baasenji could be, but also how endearing.
Then there was Ibis, who made Sugar look boring. She had separation anxiety, plenty of dogs to keep her busy, and all methods of dealing with her SA did not work. Oh well, she is the one basenji my husband and I cried as she was put down, at 16. After her, my life is so much easier.