Pre-1964, is there even any evidence that Goldwater would've had any particular appeal in the South? My understanding is that the Deep South swung in his direction in 1964 due to his voting against the most recent CRA.
Goldwater in
The Conscience of a Conservative had already written: "I am firmly convinced—not only that integrated schools are not required—but that the Constitution does not permit any interference whatsoever by the federal government in the field of education. It may be just or wise or expedient for negro children to attend the same schools as white children, but they do not have a civil right to do so which is protected by the federal constitution, or which is enforceable by the federal government."
https://books.google.com/books?id=h7s0wpc8cdEC&pg=PA28
And yes, in 1960 southern segregationists had already taken note: "Southern conservatives responded to Goldwater's affirmation in kind. Despite the fact that he had recently ridiculed Republican duplicity on civil rights, Workman praised
Conscience and its author as “one of the most encouraging books—and one of the most forthright citizens—to appear on the national scene in many a year.” South Carolina Republicans, having obtained advance copies of the senator's book, invited Goldwater to keynote their state convention in 1960. In spite of Richard Nixon's presumptive lock on the GOP presidential nomination, enthusiastic Palmetto State Republicans surprised Goldwater by naming him their candidate of choice." Jason Morgan Ward,
Defending White Democracy: The Making of a Segregationist Movement and the Remaking of Racial Politics, 1936-1965, p. 169.
https://books.google.com/books?id=yUfqCQAAQBAJ&pg=PA169