I realize that Jesus may be nearly impossible to type since a person's religious views are going to come into play even if they are not a Christian. Having said that I really think Jesus is an extravert. If you read the verses that tell you what he did on a daily basis you will see that he was usually surrounded by large crowds, and he had a following of much more than just 12 disciples. Even when he wanted to get away from the crowds for a while he would often bring his twelve closest friends lol.
Now it's true that he would also go off by himself to pray fairly regularly, but that simply shows that he is a healthy extravert. Only unhealthy extraverts feel like they need to be around people all the time. Every extravert should spend time by themselves to become grounded and reconnect with who they are.