When I started looking for a new pup last summer, it was a little frustrating. Like you, I found that shelters never had any, and I was always either early or late to the rescue table. Some breeders never responded.
Nevertheless, I kept looking and asking for referrals. Two of the referrals I received would have required me to travel out of state to go get a doggie. I was ok with that. Also learned that while most of us here are rabidly passionate about Basenjis, they’re still not a very popular breed. That means fewer breeders than popular ones. Couple that with one season/year compared to 2 or 3/year for other breeds and the number of available pups drops even more. I never knew that.
The breeders that did contact me were fantastic. Generous with time and information.
Keep looking, be flexible (age, sex, color) and you’ll find one. In the mean time Basenji proof your home, take pictures of your very secure yard, line up a veterinary and friend referrals to share with potential breeders. A good breeder will vet you very thoroughly before they’ll let a nose go. Stay positive! It will happen.