Vaisse has this great short article re: Irving Kristol and the 3 phases.
https://www.brookings.edu/articles/was-irving-kristol-a-neoconservative/
In fact, the original strand of neoconservatism didnt pay any attention to foreign policy. Its earliest members were veterans of the anti-communist struggles who had reacted negatively to the leftward evolution of American liberalism in the 1960s. They were sociologists and political scientists who criticized the failures and unintended consequences of President Lyndon Johnsons Great Society programs, especially the war on poverty. They also bemoaned the excesses of what Lionel Trilling called the adversary culture in their view, individualistic, hedonistic, and relativistic that had taken hold of the baby-boom generation on college campuses. Although these critics were not unconditional supporters of the free market and still belonged to the liberal camp, they did point out the limits of the welfare state and the naiveté of the boundless egalitarian dreams of the New Left.
The first neocons were "killjoys" opposed to all that was fun about the 60's lol...