An ancestral-and/or-lifelong R who voted for the Humphrey/Muskie ticket due to some combination of the following reasons:
1) the "favorite son" effect, if they were from Minnesota or Maine
2) the LBJ administration's and/or Humphrey's personal support for the Vietnam War
3) Humphrey's strong association with civil rights, and/or their support for the multiple civil rights bills signed by LBJ (including those signed after the 1964 election, such as the 1965 Voting Rights Act)
4) A personal approval (or personal benefitting from) Social Security and Medicare, and an appreciation for Humphrey's strong support of those programs
5) Support for some combination of other social programs which were supported by LBJ or by Humphrey (at least more so than they were perceived as being supported by Nixon). Could be anything ranging from some welfare program to something like the PBS (of course, all of this considering that this hypothetical voter backed Goldwater over LBJ in 1964, but keep in mind that the 1964 election was indeed about more than just which of the two candidates relative to the other was broadly more "pro-welfare" across the board or perceived as such).
Should note they voted for Humphrey!
Thanks, if they voted for Wallace then this would be a different subject altogether.