I think it's telling that he didn't tell Tim to scram or he even got that close of a look at all. If he wanted to get away, he could have easily done so.
The disparity is even more obvious in the pressers when reporters ask typical reporter questions, vs when someone (often Tim, but there are others) asks something technical.
Can you even imagine being Musk and running an EV company and a rocket company and having to field questions from your typical journalists? Like that Q from a journalist about why the new image of the black home at the center of our galaxy is so blurry: https://news.ycombinator.com/item?id=31353677.
Later on when he was giving that update at Starbase he mentioned the heat shield and thanked someone for a "robust" shield. I couldn't quite tell if he was being sarcastic or not.
Having said that, Musk is pretty much the worst communicator i've ever heard at the C suite level. I hope/pray he's better when talking to direct reports trying to get his crazy ass ideas and timelines done. Those poor poor people if he's not...
Musk looked bored with Tim, was often evasive, gave the appearance of wanting to get away from a fanboy.
The few times he would "open up" it was more like a recitation from someone to a disinterested audience — or as though Musk's mind was somewhere else, not really engaged or focused on the interviewer.
EDIT: Skimming the two-part interview again, Musk seems to switch between seemingly being engaged to not. Maybe it is because the interview went on really long and appears to be uncut.