Ziz said:
Um....eyes can move left to right without the head moving. We are seeing Han from the back when he says "Yeah, that'll do nicely." Maybe he's glancing at the cave with his peripheral vision but needs to stay focused on working some control on the console.

You fixed the timing of the lines, that's enough. Don't over-think the rest of it.

Oh come on. You're not telling me you only move your eyes while you're driving?

You don't say "that'll do nicely" without having a good look at it. Han turns his head towards the cave by the end of the scene, if one could edit that to happen sooner, it could work.