To a substance, the soul, not a deity. And that, actually, is an answer.
So, yeah, magic.
If what we known to exist and understand can't explain all observed data (our thoughts and inner experiences) than we are forced to infer the existence of something outside our understanding.
Yes, but there is a difference between "outside our understanding" and "impossible to understand". There is simply no good reason to believe that consciousness is impossible to understand.
Edit: also, you're describing substance dualism, not theism. You can be a dualist but not a theist.