If someone asked me whether I believe there's a God, I'd say, "The question is more complicated than it might seem. Indeed, I've written thousands of relevant pages on philosophy and religion. But basically I'm an atheist. There's no God as that being is commonly conceptualized."
That's the truthful answer that does justice to the subject, and it's the kind of answer Peterson should be giving. But he doesn't, and that's because as a psychologist he thinks he's better than philosophers and than most religious people. That's his scientistic presumption that comes across in the pattern and in the tone of how he dodges that question.
The whole pragmatism thing is actually a red herring. Isn't it possible to believe there's a God but not have the foggiest notion of how God wants us to behave? So who says the only test of a belief is in how the belief is applied in action? Do you believe there are other stars and galaxies? And how does that belief affect your actions? There are lots of beliefs that aren't directly relevant to how we live on a daily basis.
So that's just another dodge from Peterson. He either thinks the universe was created by an eternal, all-knowing, all-powerful person or he doesn't. Alternatively, he's free to admit that he doesn't know because he's still investigating the matter. But that, too, could be a dodge if the investigation takes forever so he never has to publicly admit what he really thinks, thus potentially alienating much of his fanbase.
I like that analogy of seeing water in the desert because if we're desperate we often see what we want to see. And that's the case with Peterson's fanbase, and with Donald Trump's cult. It's not just that we may or may not pick up on certain signs; rather, we read between the lines because we're not thinking clearly. We're caught up in the fallacies of groupthink and in a mass hallucination. It can take an outsider to offer another perspective.