My little ADD addled brain needs some respite at times from the monkey jungle in my cranium. I use TV and meditation for this. I don’t have to think when I watch TV unless the show is really stupid and then I have to fill the time by thinking which defeats the purpose. Shows where I am learning something or are about magical type things (Buffy the Vampire Slayer springs to mind) are usually the best.
I also do yoga just about every morning and during that time, I only count. Stray thoughts are banished like naughty children. It’s all about the numbers and maintaining the posture so I can let go and focus at the same time.
Thinking of nothing requires more effort than I am willing to put out so I don’t try too often. It becomes a challenge that is much easier met by reading (although this usually produces more thoughts), watching TV (moderately successful) or sleeping (which if my dreams are any indication your theory that the brain never shuts down would be entirely corrrect).
Seems we share some commonality with sharks in this capacity doesn’t it ? If they stop swimming, they die. If we stop thinking, just for a moment, maybe we think the same thing will happen.