A good documentary about how Ronald Reagan won the presidency is hiding within a pompous documentary, "America in Search of Itself," produced by NBC News and airing tonight at 10 on Channel 4.

The idea was to take off on themes and observations in Theodore H. White's new book of the same title, but the technique used to do that--combining a chat between White and correspondent John Chancellor with videotape from the 1980 election year--doesn't work. White keeps disappearing into the program for great stretches, so that you wonder if he's ever coming back.

But the second segment, "Strategies and Strategists," features not only White's observations on the campaign, but also those of Carter pollster Patrick Caddell and Reagan pollster Richard Wirthlin, who talk in fairly candid terms about what went wrong and what went right. Chancellor says, "Carter didn't use the advice of his pollster as well" as Reagan did, though when the two candidates agreed to a televised debate, both were defying the counsel of the consultants. Neither camp thought its candidate should boldly go to Cleveland for a mano a mano.

Carter's famous "malaise" speech gave the Reagan forces a "frame of reference," a banner to wave, according to Wirthlin; similar scenes from the two campaigns are expertly juxtaposed, and looking at the contrasts now, the Reagan campaign seems even more brilliantly conducted than it did at the time, and one wonders anew that the election results surprised anybody. Even climactic shots of the two convention finales seem keenly prophetic: on the Democratic dais, Massachusetts Sen. Edward M. Kennedy giving Carter what Chancellor calls a "perfunctory" handshake, while on the Republican dais, Reaganistic jubilation has broken out.

"That man is entirely at home in front of the camera," White says of Reagan. "He's such a funny man, such a quipster." But Reagan did not win on telegenic charm alone, White says: "He won because he had an idea," an idea people liked. Chancellor asks White if Reagan has all the qualities necessary to be president. White pauses. "I'll give you a guarded 'yes,' " he says.

The hour concludes with a visit to Saginaw, Mich., where blue-collar workers talk about Reagan, whom they still support, even as the polls show his popularity dipping to a new low. This segment adds nothing to the program and repeats material in other documentaries and evening news reports. The whole program could have been, and perhaps should have been, devoted to the campaign and the election, but NBC News was thinking loftily and, unfortunately, that too often translates on the air into thinking dull.