Hello RightWhale! I am beginning to think that consciousness is not a scientific question for the reason that it is "non-phenomenal," or an instance of "nonexistent reality." Meaning that consciousness is not a "thingly thing" or denizen of 4-dimensional spacetime that can be intended as an object in subjective consciousness, and thus made accessible to the instrumental reason, or the scientific method more generally. Rather, it is something in which we participate: IOW, we think out of, or "with the help of," consciousness; i.e., it is the matrix in which any thought process occurs, whether directed to the phenomena of the objective external world or to self-reflective, subjective processes of thought (e.g., abstract problem-solving, meditation, contemplation).
Phenomenal, existent reality is that which is studied by the natural sciences. This does not mean, however, that non-phenomenal or non-existent reality is an illusion -- just that the scientific method can gain no traction on such areas of human experience, for they do not fit the scientific method. Yet there would be no scientific method without mind, and there can be no mind without consciousness.
That is correct in that scientists have arbitrarily separated consciousness from phenomena so they may do their lab work in a narrower and more controllable environment. It was not necessary to do so; it was a judgement--oddly the very thing that consciousness does.
I do believe that mathematics may be useful in such areas because it does not require corporeal existents but rather can speak directly to organizing principles, e.g. fractal intelligence.
More importantly, theology and philosophy have much to say about Logos!