Chalmers, the author of the so-called "Hard Problem of Consciousness" bet that no such connection to the brain would be found. Chalmers won.
Chalmers is a dualist although he doesn't believe that the mind or soul is immortal as most dualists do. He does, however, believe that mind is a fundamentally different substance than matter and that it exists independently of matter.
You can read the details of the wager and see an interview with Chalmers at Mind Matters.
Denyse O'Leary who has written a lot on the debate between dualism and materialism in the philosophy of mind, discusses the wager between Koch and Chalmers and some related matters in a piece at Evolution News.
Here's an excerpt:
Materialists who insist that science will somehow “crack” the problem of consciousness often sound as though they are missing the point. The most recent attempt, the wager between Christof Koch and David Chalmers, ended not only with the materialist losing the wager but with broad recriminations within the discipline. It’s sensitive [within that discipline] because never far below the surface is the thought that all theories of consciousness are pseudoscientific.In other words, sensations, beliefs, desires, intentions and acts of will are all subjective and defy material explanation. Yet explanation in terms of the material brain is the only option open to the materialist.
As a result, the proponents of various theories are not always held to a rigid ideological standard.
Philosopher of mind David Chalmers, who coined the term “Hard Problem of Consciousness,” also spoke to Kuhn at Closer to Truth. He told him that he accepts dualism, the idea that the mind or soul has a real existence, but he does not believe in the immortality of the soul — though he would like to.
Presumably, he believes that the soul, though real, dies with the body.
He said something else too, that dualism did not come easily to him: “Every week I had a different physical theory of consciousness. None of them worked and eventually I came to see this is for systematic reasons.
"There are reasons why no purely physical theory will ever give you consciousness. It’ll always be an objective theory of objective functions. None of that ever gives you subjective experience.”