In the novel, the solar eclipse in question is the one of July 20, 1963, whose path of totality crossed Maine. In the movie, it is presumably the one of May 30, 1984, whose path of totality crossed New Orleans.
Jessie states that Moonlight Man suffers from a disorder called acromegaly which causes enlargement of the hands and feet, as well as his forehead and chin. That is also why he is so tall. Carel Struycken - the actor who portrays Moonlight Man - does actually have this disorder.
When Jessie is walking down the hall towards the Moonlight Man, there is a shot of a rooks skull hanging from his neck. This is a reference to Cuthbert in the Dark Tower series. He was known for having a rooks skull hanging around his neck.