"You don’t disappear in the sense that you cease to be as an individual mind, you are always yourself - that’s a tautology. What you lose is the sense of some identity that’s separate from what you ARE in this very moment."
This assumes that there's any concept of "you" that exists independent of your thoughts whatsoever. I think you're right that some Buddhist thinkers believe in this kind of essential awareness underlying conscious thought that you're describing, but others would say there is literally nothing underneath. "The self is an illusion", "all is emptiness", etc. If you believe in those ideas, then you have no awareness independent of conscious thought because there is no you independent of conscious thought.