I've noticed that I always use internal monologue for all System 2[0] tasks and that I've never used it for any System 1 task. As for internal imagery, I seem to be using that for both System 1 and System 2 tasks. I cannot think of any counterexamples. But if you can think of one, I'll be surprised.

[0] System 1 vs System 2 as described in Thinking, Fast and Slow