I really need to fight that instinct to make the grand sweeping conclusion - it's always getting me into trouble.

First, that intense thinking primes the brain with the info it needs to correlate.

Agree, that's what I meant by 'putting in the hours to understand the subject'

I've not uncommonly had insights during the actual working day as a result of hunching over and thinking really hard.

My best guess is that not all insight requires new mental connections - focused, analytical thinking may be capable of raising the availability of mental pathways that are already formed. This is dangerously close to equally explaining all outcomes, but I'm not proposing this as a fully general theory of problem-solving.