Bear in mind that, due to the nature of the news media and college curricula of the day, I would have had no way of knowing about any conservative (i.e., limited government) movement.
It wasn't until I started watching Louis Rukeyser several years later that I became aware of a small-government, free-market faction in American politics. This, plus experiencing a cavalcade of bad presidents of both parties (Johnson through Carter), lead me to eventually register Libertarian.
Back to your original question, the YAF was infamous on campus. They were the only known group of young people who were pro-draft; and as near as I could tell (given the media of the time), this was their only issue. If whatever conservative movement there was associated itself with the pro-draft camp, this would explain why conservativism went nowhere during this time—at least with young people.
Karl Hess, Barry Goldwater's speechwriter in 1964, attended the 1969 convention and attempted a libertarian takeover in alliance with some rogue SDS types. The libertarians included the losing John Sainsbury Objectivist faction from the 1967 convention. I later became a Libertarian Party state officer briefly until leaving the LP after Roe vs. Wade. My state YAF organization was fourth largest in the nation both in members and chapters although mine was a small state.
YAF adopted an absolutely ANTI-DRAFT position in 1967 and maintained it ever since while also supporting a volunteer military and the Vietnam War. YAF opposed Roe vs. Wade, anything associated with any Hyannis Port Kennedy, the anti-war movement, Nixon, Johnson, wage and price controls, Social Security, welfare, Medicare, Medicaid, Gerald Ford, Jimmuh Cahtuh, Billy Jeff Clinton and Obozo, and most activities of the central government, while supporting Second Amendment rights, an interventionist foreign policy, legalization of gold, military strength and hardware, and, most importantly, Ronald Wilson Reagan.
Former National Executive Director Wayne Thorburn, now a professor at the University of Texas. originally from Maryland, has published a good history of YAF, entitled A Generation Awakes.
With all due respect, I would suggest that you did not very accurately observe YAF or the Right generally in the late 1960s and 1970s AND that conservatism, while certainly including a small and limited government aspect. is and always has been about many other things of equal and even superior importance. It is a rich tapestry and encompasses a worldview characterized by William F. Buckley, Jr., Ronald Reagan, Jack Kemp, Peter Dominick, Frank Meyer, Ludwig von Mises, Friedrich von Hayek, Milton Friedman, Henry Hazlitt, Mark Levin, Russell Kirk, Margaret Thatcher, John Paul II, Robert Schuchman, Alexander Solzhenitsyn, Edward Banfield, Whittaker Chambers, Wilmoore Kendall, Will Herberg, Donald Kagan, Irving Kristol, Norman Podhoretz, Midge Decter, Domenic Armentano, William Rusher, and many, many others (whatever disagreements they may have indulged among themselves).
YAF itself was an incubator of the Conservative Movement and of a sixteen year effort to elect Ronald Reagan to the Presidency (dating from his brilliant 1964 speech A Time for Choosing in favor of an unworthy Goldwater).