The Dualist who believes in their physical existence(universe) as reality has nothing to do with the Knower or witness, with what they are aware of all the three states.
The only certain things about the three states are that they are forever changing. In contrast to the knower is the only thing of whose unchanging character one can be certain. For knower tells one about all the changes, within the waking or dream or dream experience. The one which is remaining itself relatively constant, as a standard of reference for them is the formless knower.
One can know the mind only as the universe, which appears as waking or dream and disappears as deep sleep, because when the mind (I) is there the universe is there. When the mind is absent the universe is absent.
Thus man and world are present only when the mind is present. Therefore it is erroneous to limit the mind to the physical entity. Thus searching the mind within the body is foolish venture.
Thus there is need to realize the fact that, the self is neither the waking entity nor the dream entity because the self is formless and apart and eternal. Thus the knower or witness is not the waking entity but it is the one which witnesses the three states as an object. Thus the knower is the formless subject and three states are an object. Without the subject there is no object.
Thus man and his universe exist within the object. Therefore it is necessary to become aware of the formless subject mentally because the subject also is the formless substance of the object. When one knows the subject he becomes aware of the fact that, the subject and object are one in essence.
Consciously becoming aware and learn to view the three states on the base of formless knower (witness) releases, one from experiencing the three states as reality. By becoming aware of the formless knower mentally free one from carrying the illusory baggage of burden and bondage of duality in the midst of waking. By knowing the knower (soul or consciousness) and known [three states or mind], one in essence in the midst of illusion (waking or mind) is non-dual wisdom.
Nothing disappears from illusion but one becomes fully conscious of the fact that, everything seen known, believed, experienced as person of the world is mere mirage created out of consciousness. Therefore there is no second thing exist other than consciousness. Hence it is non-dual.