The movie doesn’t dig too deep into its subject’s personal life. I remember wondering if there was a Mrs. Rogers. Her name is Joanne, and she and Fred raised two sons, John and James. They are interviewed on camera, adding detail and texture to the portrait of their husband and father. But not much is said about his childhood or his parents, though there is some mention of bullying and other early hardship. Mr. Neville, whose other films include “20 Feet From Stardom” and “The Best of Enemies” (directed with Robert Gordon) is not interested in psychological sleuthing. Rather than trying to unlock offscreen secrets, he sets out to assess the meaning and impact of an onscreen persona.

It is that emphasis — the earnest, critical attention to the public Mister Rogers and his legacy — that makes “Won’t You Be My Neighbor?” feel like such a gift. Like Tom Junod’s great 1998 Esquire profile — the inspiration for a Mister Rogers biopic with Tom Hanks set for next year — this movie is at once unapologetically admiring and intellectually rigorous. (Mr. Junod shows up to add a few new insights and anecdotes.) It begins with an old clip of Fred Rogers, a trained composer, at the piano, explaining his approach to communicating with children by way of the musical concept of modulation. Some changes of key, he says, are easy enough to manage, while others are trickier. And so it is with feelings.

Several generations of American kids learned letters and numbers from “Sesame Street,” phonics from “The Electric Company,” and civics and grammar from “Schoolhouse Rock!” What Mister Rogers tried to teach us — how to navigate “some of the more difficult modulations” in everyday life — might now be classified as emotional literacy. He acknowledged that anger, fear and other kinds of hurt are part of the human repertoire and that children need to learn to speak honestly about those feelings, and to trust the people they share them with.