Strictly speaking the Bhagavad Gita though revered as a sacred text is not regarded in the same light as the Vedas and the Upanishads and the Vedanta Sutras. They are collectively known as the Triple Canon. Shankara wrote a commentary on the Gita bringing out the deep philosophical implications of the text. It runs to over 800 pages in the translation by Swami Gambhirananda published by Advaita Asrama. Chap. 13 is on the topic of the ‘Field and the Knower of the Field’.
13:2
“And, O scion of the Bharata dynasty, understanding Me to be the ‘Knower of the field’ in all the fields. In My opinion, that is Knowledge which is the knowledge of the field and the knower of the field.”
As pure being Brahman pervades all existence as its being. How is it that we do not know this?
“This being so, the Knower of the field, who in reality is God Himself, appears to have become a mundane soul owing to the various adjuncts which are products of ignorance; as for instance the individual soul becomes identified with the body etc.”
Shankara gives various examples of how this sort of superimposition takes place. In low light a stump of a tree might be mistaken for a man but that does not mean a man is a stump of a tree. What the analogy tries to bring out is that our identification with the body is that sort of mistake. Shankara does not explicate the full doctrine of adhyasa/superimposition. That is in the more abstruse commentary on the Vedanta Sutras. In short what I interpret him as saying there is that this ‘error’ is what makes perception and knowledge posssible. The perceptuality of things is based on the unity of being which allows the object to be present to the consciousness of the subject as that object is. It can be superimposed because of the unity of the substratum.
In this commentary he also revives the objection : is not the mixing up of things that you propose as a standard analogy be due to their similarity.
That is different from the body and the self. Here you have a single unitary experience.
“On the other hand, in the case of the body and the Self, the mutual superimposition occurs verily between a knower and an object of perception. Thus the illustration is not equally applicable. Therefore may it not be that the properties of the body, though objects of knowledge, belong to the Self which is the knower?”
Here the objector is making the standard mistake of taking a focused analogy which is meant to bring out a metaphysical concept via an everyday occurrence and generalizing from it. An analogy has limited scope and breaks down if we overextend it.
Shankara’s response to this is that when you so identify the Self with the changeful, what Hume called bundles of perceptions, you accept that the Self is mortal and transient. In his Upasdesa Sahasri he presents the argument against the identification of Consciousness with a state of awareness. When we awake from Deep Dreamless Sleep (Sushupti) we are aware that we have been asleep even though there were no contents of consciousness during that state. A profound argument which I have written on in several posts, topics below.
Superimposition of the changeful on the changeless is the most significant error that human beings fall into it. To cease to do this is to have achieved liberation/moksha.