I’ve noticed that Eugene has a tendency to clear his throat right before launching into a speech. In the first gif, it’s right before, “I know not who you are, nor how I came to find you...” In the second, he’s about to say, “You know, I can’t help but notice, you seem a little at war with yourself here.” The third one fits right between, “ Hey, the sideburns are coming in nice, huh? Gotta be excited about that,” and, “ Anyhow, just wanted to say, I shouldn’t have split...”

It seems to me that the clearing of the throat is not just to prep for the speech he’s about to give, but also to get into character. In the first and third, it’s more obvious that he’s been taken by surprise, that the Flynn has been briefly knocked out of him, first by this mystery girl with the long hair and then by the one Stabbington glaring at him for daring to try to make light conversation.

But in the second scene, it’s less obvious. He’s extremely pointed when he clears his throat. This, I believe, is because it was genuinely Eugene who was so utterly irritated by Rapunzel’s bi-polar antics. By the time she’s sobbing (yet again), he’s tired of this nonsense and ready to move on with his day. So it’s Eugene who plods up to her, completely unamused, and gets himself into the role of Flynn so he can try to smooth talk his way into getting his satchel back.

As a bonus, here’s his face, even as he clears his throat: