This is exactly how I 'work' and always have. Sometimes the process of distilling a solution in my mind for some more difficult problem can even take days.

But the common denominator is that it happens away from the keyboard and is not visible to an outside observer.

At the keyboard I work on different, easier stuff in the meantime and regular go back to the difficult problem in my mind when doing mundane things.

Walking is a favorite. Forests/nature works best, parks are fine. City is kinda ok.