Consciousness does not identify with anything
I sometimes hear people claim that pure consciousness identifies itself with the ego, with thinking, or with the body. What they are effectively saying is that the pure Self, i.e. that which is conscious of all experiences, believes it is a separate self, a thinker, a chooser, and doer of actions. But the pure Self, does not believe or think anything. It is that which is aware of the thoughts and beliefs that are arising—the "knower" of all experience.
This Self is not tainted or affected in any way by the perturbations of the mind. It's essence remains unchanged, just as the water in a wave is not itself changed by the wave's motion. Unchanging, the Self is the silent knower of all that appears in our experience.
What is actually happening is that the attention becomes absorbed in the thought-system of the ego.
Attention is intrinsic to being aware. It might be thought of as the spotlight of awareness, focusing on one particular aspect of the enormous breadth of the totality of our experience. It's job is to attend to things that may be important.
The attention has two basic modes of operation. There is a relaxed mode where everything is OK. We are at ease, and the attention moves effortlessly, from one possible interest to another, with no voluntary effort or control—attracted to the sound of a bird, an itch, a moth flying by. In this mode, our attention is not pre-occupied with who we are, or our sense of self.
Then when we do notice something of interest our attention stays there for a while. We pay attention. We consider whether this may be important for our well-being? Do I need do anything? If so what? The focus of consciousness is now on the issue at hand, and the thoughts we are having about it.
If the issue at hand is deemed important for our well-being, then the seamless whole of our experience is divided in two. There is this body, the organism that needs taking care of, and the world around that may need to be changed in some way, or conversely be prevented from changing. We create a sense of being an individual self who is thinking and acting in the world. But this sense of self is, in the final analysis, just a set of thoughts and beliefs. It is another form arising in experience, another "thing" we are conscious of.
Consciousness has not identified itself with this sense of self. The identification is in our thinking. Consciousness itself remains, as ever, the silent witness of all these shenanigans. It is simply aware of them as it would be of any other thought or experience.
The separate sense of self is like a character in a novel. If it is an engrossing novel, we, the reader, can become so absorbed in the story, the ups and downs of the hero's adventure, that we temporarily forget we are the reader of the story. Our attention is absorbed by the drama, imaging the world of the hero. Similarly with the dramas of our own lives, our attention becomes absorbed in our own hero's journey—the challenges and opportunities, our hopes and fears, the choices we must make, the risks we must take. But the pure Self, the knower of all experience, has not identified with the separate self, the character in our personal story. It merely experiences the machinations of this particular way of thinking.
So when we say consciousness becomes identified with the ego, with thoughts or the body, what is actually happening is that the attention is so focused on these aspects of our experience that they dominate our experience. For a while, the fact that we are much more than that does not get a chance to enter. We forget we are that which is watching the drama unfold.