Puttering is the name I tend to give this process; apparently that's the more American word for it. UK usage favors pottering. The OED defines the verb potter as "occupy oneself in a desultory but agreeable manner; move or go about whilst occupied in such a way." The Online Etymology Dictionary adds "be busy in doing little," and notes that it seems to be a frequentative verb, similar to chatter. (Which suggests that fretter might be the verb for pottering with a guitar—if we didn't already have noodle.) It also includes a graph showing that usage of potter is about half what it was in 1800. I wonder how that graph might align with the spread of models of industrial productivity.
I, for one, have not had much time for puttering lately. I miss it, and I'm pretty sure my creative work is suffering for the lack. The sticky-note wall might qualify, since it is fundamentally aimless. But that's no more than a minute or two a day. A minute is not a lot of downtime.
I just encountered Hanif Abdurraqib's description of an annual braided-vignette document on a random topic of interest, which can grow to hold a book's worth of words that will never be public. I love that idea, and I'm curious about what the songwriting equivalent would look like. Perhaps a rhyme/stanza game within the St. Jerome's document? The band's goofing around with parody songs and Unbelievable Truth mashups might serve a similar function. Certainly digging in to etymology does.