It kinda seems like that's what you advocate for here, but I could be wrong. At least, on first read that is.

In any event, that Creative Brain doc has a section which uses toy blocks to demonstrate that mentally non-demanding 'busy' tasks can be a boon to creative thinking, as opposed to sitting quietly or performing complex mental activities.

Doodling seems like it would fit the bill. If one is well practiced at knitting or cross-stitch, doing that can work. Anything which doesn't require a strain on the brain, I suppose...but that's a relative measure...