What is self-attentiveness?

A couple of weeks ago a person called Jon posted the following comment on one of my recent articles, Self-attentiveness and time:

I’m having a hard time understanding exactly what Self-attentiveness is. I just don’t see where the ‘attentiveness’ part comes from. The way I understand it Self-attentiveness is the practice of simply remaining without thought while not falling asleep (being keen and vigilant to prevent any thoughts from rising). However, as I noticed, Sri Ramana says this isn’t so because if this were the case, one could simply practice pranayama [breath-restraint], and Sri Ramana said that the effect of this was only a temporary subsidence of mind and not the annihilation of it. So getting back to my question, what am I supposed to be attentive to? Self. Well what is Self? Self is the I thought. Unfortunately, I can’t find this I thought anywhere! How am I to be attentive to it? Please elaborate. As I said earlier, the way I understand Self-attentiveness currently is simply being keen and vigilant not to let any thoughts rise. Yet I don’t think that when I remain without thoughts I am being self-attentive, because when I remain without thought I am actually not paying attention to anything! (I believe) Yet, isn’t the goal of self-attentiveness merely to destroy all thoughts? Can’t I do that without focusing on some obscure “Self”? Am I supposed to be additionally Self-attentive? If so, can you please really break it down for me so that there is absolutely no doubt as to whether I’m doing it right?

In reply to this, an anonymous friend wrote another comment:

“Am I supposed to be additionally Self-attentive? If so, can you please really break it down for me so that there is absolutely no doubt as to whether I’m doing it right?”

With reference to the above comment of John, I might state that self-attentiveness and eschewing thoughts would constitute a unitary process, there being no additional self-attentiveness over and above not paying attention to thoughts.

Jon replied to this answer in his second comment, in which he wrote:

Thank you anonymous for your comment. Just to be clear, you’re saying that the sole purpose of self-attentiveness is to ignore thoughts, therefore if I simply ignore thoughts I would be Self-attentive? Michael’s opinion on this would be greatly appreciated as well.