Sure, our friendly neighborhood narrator likes to keep his distance, but every once in a while, he'll cozy on up to a character and give us a glimpse into his or her thoughts.
Take this moment, when we get to see what Jody's thinking: "He felt an uncertainty in the air, a feeling of change and of loss and of the gain of new and unfamiliar things" (1.14).
Or this one, where we get to know Billy's mind: "He had no right to be fallible, and he knew it" (1.106).
Even the red pony gets his day in the sun: "The pony talked with his ears. You could tell exactly how he felt by the way his ears pointed. Sometimes they were stiff and upright and sometimes lax and sagging. They went back when he was angry or fearful, and forward when he was anxious and curious and pleased; and the exact position indicated which emotion he had" (1.70).
This narrator really knows his stuff. He can jump around from character to character when the occasion calls for it. Still, he mostly sticks with Jody. This is Jody's story after all—he's the youngster with all the growing up to do, and it's him we're closest to as we read.