Hi Julian,
People who teach concentration meditation (samatha jhana, the purpose of which is temporary abatement of mental hindrances in order to develop a calm, focusable mental state for studying mental states and phenomena) have many different opinions on your question.
I recently started listening to the nun Khema and there are many recordings and videos of her talks available online.
She mentions stabilizing the first three jhanas for something like 15 minutes to get a sense of them (getting a sense of them is not to be confused with mastery, not that you would). She also mentions one departs from the object after the first jhana is stable and that one moves to the sensations themselves (piti, sukkha).
So while she mentions to move the mind to the sensations of piti and sukkha when they arise, I agree with you that returning to the breath is the useful idea when those jhanas do not move into the next jhana, but instead come back up into the unconcentrated mind. Some people like open awareness or noting, but for me I find that open awareness and noting can train the mind in too much mental searching for stimuli (sounds, lights) and that one anchors the mind to the breath again and again like rocking a not-quite placated baby. Fourth jhana cannot arise while the mind is even slightly provoked, self-interested or wanting. The mind really has to be "rocked" into an alert, wakeful calm and I think adhering the mind to the breath does that.
That's how I experience it. Most importantly is your own experimentation though. Good luck. It will be nice to read what you find, too.
