"Getting Beyond Conceptual Understanding to Experiential Understanding (Awareness of Awareness) . . . ?"
Initially, the words "awareness awakens to itself" or "what is" awakens to "what is" . . . almost make sense to Mind . . . but not quite. What do they mean, it wonders, and what are they referring to?
First, understand that to fully explore "awareness awakening to itself, etc", one has to personally experience and recognize "experiential awareness" for what it is and isn't. Meaning, without basic experiential (nonconceptual) understanding one remains ensnared and bedazzled by "intellectual knowing, conceptual knowledge". (The fact is, Mind cannot think or reason its way to Awareness.)
So how does one realize this basic experiential nonconceptual understanding? Well, as Nisagardatta Maharaj points out (herein paraphrased), "The very act of perceiving reveals I am, you are, we are not what is perceived." (In other words, experiential awareness is innate in the act of perceiving.)
However, I'm not going to explain or analyze the meaning of Nisagardatta's words for you here but only suggest . . . a mental pause . . . between "thinking" about a response to his words and "directly perceiving" Awareness. (Remember, the "reveal" occurs in the moment of perceiving, not in 'thinking about' what is perceived.)
So, if you hear thoughts in your head right now then note you are not these thoughts. If you feel bodily sensations right now, realize you are not these bodily sensations. You are That which is Aware of them . . . ever present Awareness unnoticed by Mind. (If this sounds a bit abstract, than it is, but what's referred to is living presence itself.)
Right now you are either "aware of awareness itself" or "querying what awareness is suppose to feel like, look like", etc, etc, etc. (In other words, still mired in Mind.)
If this is so, we'll try one more reminder? Consider . . . "what is" is formless, but manifesting as this biological form sitting in front of the computer, laptop or tablet screen "what is" is "embodied awareness". (Mind may want to explore or dispute this assertion but don't indulge the impulse.) Observe only and directly perceive Awareness . . . energetic, alive, and immediate . . . prior to any thinking. This is nonconceptual awareness. (Notice: there is nothing for Mind to hold onto in this energetic alive awareness; it's all flow, no boundaries.)
In this direct perceiving it is seen that all pointing words are irrelevant to "directly perceiving". It is seen Awareness is experiential (embodied) even though it is not an experience.
As such, feeling pain is not awareness, being happy is not awareness, laughing joyfully is not awareness. However, That which is aware of bodily pain, emotional happiness, and joyful laughter is what we are in the moment. . . embodied Awareness.
But remember, ultimately it's not what I say, or what Nisagardatta or Ramana says, or what anybody has to say about Awareness, etc, that counts, what counts is that you directly perceive (unmediated by thinking Mind) how it is that you see what you see . (Yes, these words are examples of Mind spouting illusory knowing, so ignore them . . . just see!)