In a similar vain, I currently enjoy reading A Philosophy of Walking by Frederic Gros. Gros draws the musing of various philosophers on walking. To me, his description of the slow beat of the footstep that propels imagination resonates with how walking works for me. When I'm stuck on something and feel I need to keep pushing towards a solution, a short break, often the result of an obligatory walk/ride to the train station, already sets my mind in motion.

Crucial is that the walk is not an intentional break for the purpose of brainstorming, because then my thoughts stay stuck. Such walking is 'idle' in the sense that it is an almost automatic process. The whole point is that walking/idling should not be a productivity tool.