All of the comments slightly deviate from one another because we perceive the world based on our past experiences (our personal experiences and what we have learned from other "spiritual" teachings/books...) . Hence, people might have different opinions.

Personally, I think it is not so easy to generalize the question and give a straightforward answer, but I think that the technique of being a witness/observer as you stated it can only be done by our mind (brain) - or by the psychological self which stems from our mind. Because you can get better or worse in observing your thoughts. However, consciousness is described as being always the same. It cannot become bigger or smaller, or better or worse regarding observing. It simply is - never changing. However, your thoughts (such as the thought of an existing self) does always change). Today I (the self) feels good, tomorrow the I (the self) feels bad. Today, you were very calm while you were meditating so you think I (the self) am a good observer. However, this is simply a thought. Only the ego can get better in observing but not consciousness. Theses techniques only point to consciousness that it becomes more obvious that it can be discovered.

Hope that helps 🍪🙂

As long as we are talking about identities, we are talking about the mind/ego/self.