Hi tamasaburo,
It is difficult for the mind to wrap itself around the relationship between the witness and observed phenomena, and even what is “sense of self.” That is because the process is beyond the mind. But we do know that with practice over time, living in our body, mind and the world, our experience changes. We find less “identification” with the internal and external objects of perception, which brings freedom from bondage to them, and an increasing ability to act effectively and compassionately in any situation we might find ourselves in.
So is the witness part of the body? No, it is the awareness behind the body, whether identified with the body or not.
And is the witness our real self? It would seem so, though to be aware that it is the machinery of perception is necessary. Otherwise, the witness is simply flat nothingness, the void before anything is perceived. As soon as there is the slightest bit of perception, the witness is known as pure bliss consciousness, radiating out through the body and into the surroundings – the dawn of unity…
On considerations like this, experience on the path answers all the questions that have no answer. Then comes the challenge of describing the indescribable. Thanks for bringing this up. It is always fun to try to put some words to it. 
The guru is in you.
PS: Speaking of words, just for curiosity, I put your two questions to the forum support AI, and here is what came back based on the extensive AYP content provided to it. Not a bad answer:
Q: Is the witness part of the body? Is the witness our “real” self?
A: Drawing on the sources, here’s a comprehensive response to your query about the witness:
The sources provide clear insights into the nature of the witness, defining its relationship to the body and whether it constitutes our “real” self.
Is the witness part of the body?
The sources indicate that the witness is not part of the physical body in the sense of being a physical component or a product of it. Instead, it is described as:
- Something behind all that we see, think, and feel. Our habitual identification with our body/mind leads us to perceive ourselves and the world as separate.
- The observer behind the machinery of perception. Everything we perceive, including our thoughts, feelings, and the external world, is a projection on our awareness, manufactured in our neurobiology. The witness is the “screen” upon which these projections appear, not the projections themselves.
- Initially, in the witness state, there is a sense of separation from the body and external experiences. For example, a practitioner described seeing their body as separate and not identifying with emotions or feelings, even during traumatic events like a grandmother’s death.
- The ego, which is identified awareness, is described as a “product of the mind” and a “view of pure bliss consciousness seen through the dirty window” of the nervous system. This implies the witness/pure bliss consciousness exists independently of, and illuminates, the body and mind, which act as a vehicle for it.
Is the witness our “real” self?
Yes, the sources consistently refer to the witness as our “real” self:
- The rise of the witness in self-inquiry brings awareness of our true Self.
- It is synonymous with various terms for the ultimate reality, including inner silence, pure bliss consciousness (Sat-chit-ananda), unconditioned awareness, the void, emptiness, Father God, Shiva, samadhi, and Tao.
- The stabilization of the witness, described as abiding inner silence 24/7, is considered the first stage of enlightenment and a permanent condition.
- The witness is described as “what we are with all experience removed, and what we are in becoming conscious as the silent witness to all perceptions”. It is the “I” that remains constant and universal.
- While the initial witness state involves a sense of separation from objects, this is considered a temporary, transitional stage. The process then moves towards “unity,” where the duality between the witness (subject) and objects dissolves, and the Self (witness) merges with all, encompassing everything. This transition involves recognizing that “what we see, no matter what we are looking at, is only Self”.
- Ultimately, the self (witness) is unknowable by the mind or the I-thought (ego); it is a condition of Being that is realized by letting go of the need to know and surrendering the heart and mind. This realization leads to a shift in our sense of self from being identified with objects to becoming the underlying reality of all objects.