Davinci is a cutie, and I do think he might have some Basenji in there!
Refusing to go out in the wet is certainly a Basenji trait; I just started using a "Potty Park" http://www.pottypark.com/ for my 15 year old Basenji (who is recovering from a probable stroke) so he won't have to go out when it's way too cold. Maybe you'll want to give that a try for Davinci when the weather isn't so good.
So far my Billy will pee on it when it's outside but not on it when it's indoors. We've had it less than a week and we've worked our way up to it being just outside the open door. I'm confident that this old dog can learn a new trick.
-Joanne