Yamazaki is the childhood friend and the best friend of Chiharu. He is also a friend of Sakura, Tomoyo and Syaoran who has a hobby of telling stories or histories of whatever is in the topic. The only person who can stop him with this hobby is Chiharu who gets annoyed when he starts telling stories which Sakura and Syaoran always believe. He and Eriol likes to fool around a lot with these histories that he makes up and Eriol backs them up.
You would not see his eyes open. Ever! You would only see that opened in one of the special episodes of the anime when Chiharu stepped on his feet while he was telling a story to Sakura and Syaoran, which again, they believed and had a theory that whenever his eyes open, he is telling the truth.