Goldwater used it in 1964 in campaign material/ads he ran in newspapers but never as his official slogan.

Clinton said it in a speech in 91.

I haven't found any pictures, but I could swear that the Dixiecrats used it too. Can't find it tho.

Did he ever claim to come up with the slogan himself?

yes, he did. even tried to trademark it

I don't think so, but have he ever gave Reagan credit?

Just like Biden at heart ♥️