I routinely get up and leisurely pace about my house for 5 to 10 minutes as I work on something, thinking it through in my head and then coming back and putting it down in code in a burst (currently working from a home office, not as applicable for someone stuck in a cubicle). Also works extremely well when I'm stuck on something and it doesn't require a large amount of distracted time (ie I don't have to go take a hike in nature for an hour in the midst of work). And of course sitting and staring at the problem is the absolute least effective approach. Also has the benefit of at least somewhat countering the negative health effects of persistently sitting for long stretches.

I agree that staying in the same room seems to have a considerably lessened benefit (seems to reduce the benefit to almost zip). I have to leave the room, just getting up and standing about in a small space doesn't do it.