My first female, who was never neutered and died young used to pee on our bed when my husband had been out of town and returned. Happened a few times till she got used to it going on.
My current female is neutered and has only peed on the bed once and I’m pretty sure she had tried to tell us she wanted to go out.
I think Basenji’s are much harder to train to go out then other breeds. But with persistence I believe it is possible.
If your boy is not neutered I would start there, and until then I agree that diapers would save you a lot of extra work.