Quite the interesting but unapproachable topic. Doesn't help that neurology logic on brain-level is dynamic and general rules are hard to extract.

And sometimes to not think. Taking a walk is a great way to clear ones head.

but sometimes I need a little burst of the phone/music to serve as a distraction and force me to unplug from the hard problem that i'm fixated on. once i've successfully started thinking about something else, phone/music off and let the productive mind wandering begin

I find that even if I use my phone while walking I will eventually stop paying attention to the phone.

The hard part for me is stepping away when I'm grinding on some problem. It always feels like I'm sooo close and this next idea could be the one that lets me walk away victorious.

Usually I'm wrong though and taking a break would be a much better use of my time. Walking, biking, noodling on my guitar, or even going for a drive all seem to work for me.

I find that I have more time to be a dreamer and let more interesting solutions unfold in my mind. After that the planning and execution is much faster.