First, congrats to your son for making it this far. That in itself is a wonderful accomplishment, and an honor to be considered for something so significant. Of course an introverted kid might not be comfortable discussing his own accomplishments, especially with strangers. So, get him used to saying “Thank you” in a loud, clear voice, because it is very likely that the first thing the interviewers will say to him is “Congratulations” for making it this far, etc. If your son can learn to hear himself handle the “Thank you” part, he may be able to relax a bit and gain his confidence.
Even if he is an introverted kid, it does not mean he’s not deserving. They want to interview to him for a reason. Have him try to determine why they want to talk to him - what makes him special. It may be obvious at first, if purely based on grades or scores, but the people who tend to do well at this sort of thing are the people who can convey their appreciation for the people who helped get them there so far, but also an appreciation of the fact that there is still so much out there for them to learn, and perhaps an excitement to be able to help others learn along the way.
There is also something to be said for the ability to smile through your nerves. The ability to directly answer questions, but maintaining a friendly conversational style, usually helps.
An introverted person is often quiet, especially about the unknown. However, you can remind him that this whole experience is about a topic he knows more about than anyone else on the planet - himself.
Do you know if he is one of 2, 3, 5, or 20 possible candidates? Remind him that even if he does not win this prestigious scholarship, this experience will undoubtedly help him. Don’t tell him things like “Not to put any pressure on you, it’s only your entire future that depends on how you do in this interview.”
Now for the practical advice, in a 2 day marathon interview, I would want to make sure he packs good antiperspirant/deodorant, brings a good toothpaste, and that he wears comfortable shoes - if they are new shoes (it is not uncommon for HS senior boys to need new shoes every month or so) , then be sure he has a few days to break them in. And for god sakes, do not feed him beans the night before his interview, or anything that could make him gassy. Sometimes, telling a kid a reminder like that can ease a lot of tension.
Be proud of him. You know your kid - and you will know whether that means you need to show him you’re rooting for him, or to play it low key, treat it as just another of the many wonderful recognition he has earned. Maybe tape a copy of the letter to the fridge, where you used to put his grade school drawings / homework / report cards, will be enough to show him you’re proud of him, but not making too big a deal about it. But by all means, bake cookies for when he returns home mentally and physically exhausted from the process.