Sorry in advance for the length of the response, but baseball is something I've learned a LOT about over the last 10 years :) Happy watching, the fun is just beginning--every year is more fun than the last, watching the kids & their skills grow just amazes you in hindsite!
**Ask him what he does to "get in the zone" at practice & remind him about it before the game. It may sound a little rich for his age, but give it a try...my son has played for 10 years, and he ultimately just got to the point where he tuned everything else out. As they get older, they learn to watch the coach for their sign & then wait for the pitch...this along with their silly antics at the plate become a ritual in itself. If he doesn't "know how", help him find a way to tune out everything except the coach & most importantly the ball. There's a baseball movie (besides The Sandlot) that my kids watch over & over...might be the Bad News Bears (the name escapes me for sure) where the kid plays like a superstar when he's listenng to music on his headphones("I love it when you call me big poppa), and not so well otherwise. The moral is that if you find a way to take your mind off of it, you can make an enormous amount of pressure whether internal or external go away.
**The coaches/league may look down upon gum depending on where you play, but sunflower seeds are a good idea AND make them feel more like the big kids.
**Remember to tell him (privately of course) that you believe in him and that no one will be upset with him as long as he puts forth his best effort. You would not BELIEVE how those boys can get into each others heads in the dugout...urge him to encourage the others to do their best both batting and on the field, it helps strengthen the team and works on all of their self-esteem especially when their peers are supporting each other.
Have Fun!
