Billy
The protagonist whose coming of age is facilitated by his three trips into Mexico in the 1940's.
Boyd
The more rash of the two brothers. Instead of sharing Billy's curiosity, Boyd is rather arrogant and combative. He doesn't learn from his mistakes, and his mouth gets him in trouble with others.
The father
Billy and Boyd's patriarch, whom Billy admires for the elegant way he controls his environment.
The Catholic man
There is a cast of minor characters that help Billy by sharing their personal philosophies about life. The most important of those is the man Billy meets who explains what he learned by converting from Mormonism to Catholicism: that religions are all basically all the same narrative structure expressed through myth.
The gypsy
There is a gypsy who comes along to help Billy after he is attacked by evil men in the desert.
The wolf and the dog
The characters of the wolf and the dog are important because Billy treats the animals as if they matter, like people even, one might say. Whether they constitute 'Characters' or not is fascinating, but regardless, they do demonstrate the Messianic archetype—a wounded animal and a predator.