In some far eastern traditions mindfulness of the mindfulness, or awareness of awareness itself, is deemed a deep significance. Its supposed to signify a deep level of insight, akin to enlightenment itself. It may have connections to a thoughtless or ‘no-mind’ scenario. Koans are said to lead to such a state of awareness. ‘What is the sound of one hand clapping’, and the student is unable to give rise to such a thought, to visualize that sound.
However I often felt that this pointed to an absence of material phenomena, a form of emptiness -it cannot be said to be an absence of mind as the mind is present. It’s formless nature could be the start of the ‘base of emptiness’ or the ‘base of consciousness’. These are states of formless absorptions, as mentioned in the Pali texts, not enlightenment itself.