I always considered 'neoconservative' as referring to those classic democrats who, seeing the political handwriting on the wall, joined the 'conservative movement' in the wake of Reagan's obvious success.
If I remember right, the first of those thinkers to be called (or to call themselves) neoconservatives in the 1970s were Nathan Glazer, Irving Kristol, Jeane Kirkpatrick, Seymour Martin Lipset, Daniel Patrick Moynihan, Norman Podhoretz (who steered
Commentary away from the left during that decade), and Ben Wattenberg. (His book,
The Real Majority, is thought by some to have been the earliest neoconservative argument in full book form.) Their turns toward it began when the New Left drove them to endorse Washington Sen. Henry Jackson for the presidency over South Dakota Sen. George McGovern in 1972, seeing McGovern as a New Left co-opting and Jackson as anything but, especially in foreign policy. The socialist intellectual Michael Harrington first hung the tag "neoconservative" on them, but Irving Kristol fashioned it into a badge with his famous remark about a neoconservative being a liberal mugged by reality and in his 1979 essay, "Confessions of a True, Self-Confessed Neoconservative"---written in response to Peter Steinfels' book-length attack on the early neoconservatives. (Kristol, in fact, called his second anthology of writings---his first had been, of course,
Two Cheers for Capitalism---
Reflections of a Neoconservative in 1983.
The original neoconservatives themselves weren't exactly a movement. The aforesaid Irving Kristol essay included another once-famous wisecrack, "When two neoconservatives meet they are more likely to argue with one another than to confer or conspire." James Q. Wilson, himself an early neoconservative, noted that those neoconservatives had no "manifesto, credo, religion, flag, anthem or secret handshake." And none of those original neoconservatives ever argued with that.