Brain activity appears, to all possible means of detection currently available, to be completely linked to ‘thought’ on a one-to-one basis. The relationship in detail is not yet understood, true. But until there is a even a single piece of evidence that thought can exist independently of brain activity, believing that it can is a large and baseless assumption, albeit not one that can be disproved. Because as I tried to say earlier, it’s impossible to prove a negative. We could study braindead coma patients for a million years and find no evidence of thought, but we still can’t say that proves there’s no thought in a braindead person because there’s no way of knowing for sure that tomorrow there won’t suddenly be some evidence in the form of a braindead person developing the ability to use poltergeist activity to write something down or whatever. That’s why the burden of proof is on the assertion that something exists or is possible, not on the alternative that it doesn’t or is impossible, because they are logically unprovable. So if dualism implies that thought is possible without brain activity, then the only logical response is to remain sceptical until some evidence is presented.
As for God, it’s true that there can never be such a thing as evidence that some form of undetectable, intangible, omnipotent being didn’t or doesn’t exist outside of the realms of human understanding. But as yet He hasn’t provided any decent evidence for his existence either, so there’s exactly as much evidence in support of that as there is to support that the Giant Flying Spaghetti monster created the universe, or that we all exist in some author’s mind on the real Earth, or that no supernatural will was involved at all in the creation of the universe but some as yet poorly understand natural process (like the ekpyrotic theory). As above, there’s no way to prove that God, the Spaghetti monster, the Author don’t exist, but certainly no evidence that they do either. Since there’s nothing to choose between any of those beliefs in terms of provability, I tend not to believe any of them (but certainly not in any kind of supernatural entity - I don’t see anything more reasonable in any of the Gods of the religions of the world than the Flying Spaghetti monster), but remain interested in the theories of physicists because at the very least I have more respect for the scientific method of trying to find out what’s what and prove your theory with some evidence than in simply accepting that the answer is something I’m told by what someone wrote down in a Holy book or someone who’s had some unlikely revelation.