A lot of productive thinking happens when asleep, in the shower, in flow walking or cycling or rowing.

It's hard to rationalise this as billable time, but they pay for outcome even if they act like they pay for 9-5 and so if I'm thinking why I like a particular abstraction, or see analogies to another problem, or begin to construct dialogues with mysel(ves|f) about this, and it happens I'm scrubbing my back (or worse) I kind of "go with the flow" so to speak.

Definitely thinking about the problem can be a lot better than actually having to produce it.