I sometimes find myself noticing unasked questions when I try to rigorously prove (or just make a convincing argument for) something obvious. And I find myself looking for proofs and/or convincing arguments when I try to generalize something obvious to something not quite so obvious.

Good examples of this can be found in the famous thought experiments of theoretical physics - Maxwell's demons, Carnot's engines, and Einstein's moving observers seeking to synchronize clocks. Examples in the analysis of rationality can be found in the thinking leading to the famous axiomatic characterizations of rational decision making - von Neumann's rational utility maximizers, Nash's rational bargainers, Rubinstein's impatient variant bargainers, and Harsanyi's empathetic utilitarians.

But moving now to the meta-level: You mention two questions - how to ask the right question and how to notice there is a question to be asked. You suggest that the second of these is the true 'right question'. May I suggest that perhaps the best question is "how do you know that you are asking the right question once you have discovered the question?"

Which thinking just draws you in deeper. The 'right' question, to my mind, is the fruitful one - the one that allows you to make progress. But then we need to ask: what do we mean by progress? How do we recognize that we are making progress?