Scientists cutting into a living brain and finding the interface points, brains doing physically impossible computational feats, physical systems behaving differently in the presence of brains. Hard to say more than that in the absence of specific predictions.
I gave a prediction in my other comment. Do you agree that the continuing absence of a substantive reductive theory, or even an adequate approach to a reductive theory, of phenomenal consciousness is (weak) evidence against reductionism? If so, do you consider it (weak) evidence for dualism?
Also, not all dualists are substance dualists. Chalmers doesn't believe that brains are getting signals from some non-physical realm.
In Zombies! Zombies? Eliezer mentions that one aspect of consciousness is that it can causally affect the real world, e.g. cause you to say "I feel conscious right now", or result in me typing out these words.
Even if a generally accepted mechanism of consciousness has not been found yet are there any tentative explanations for this "can change world" property? Googling around I was unable to find anything (although Zombies are certainly popular).
I had an idea of how this might work, but just wanted to see if it was worth the effort of writing.