Given your specific question about turning off your thinking, I think the two responses that people gave to otherwise occupy your brain are probably the most helpful. You need to find something that interests you, can potentially take a while to think through, & is at the same time a little dull (by this I mean it in no way gets you stressed or excited) or offers avenues that you can dwell on (for example both for golf & state capitals, you can start remembering the scenery). Both posters, the round of golf & the state capitals offer all of the qualities. I do something similar & it helps. I am interested in history so I can start listing the causes of the Wars of the Roses or the First World War, or listing English Monarchs & any details about them or US Presidents. On the other hand if politics gets you upset don't try the Presidents thing.
But anything along these lines will do. You could take apart an engine & put it back together.