It might be arguable that the check-in on the problem isn't so much an automatic process, but one of stimuli triggering a pattern match on a problem, or conscio

It might be arguable that the check-in on the problem isn't so much an automatic process, but one of stimuli triggering a pattern match on a problem, or conscious triggering of the thought process. When people are working on a problem, simply saying out loud "I'm trying to work out this problem" has an effect lighting up the neurons associated with the previous thinking done on that topic. If there is new information, (like a snake eating its tail), that may be integrated unexpectedly into the consideration. I would suggest that there are prompts all around us that will trigger a "revisit" of a problem, it is conscious (or at least autonomous based on stimuli) action, but not directed.