Well, my ears may not be so good, but using good earphones at a decent volume, I still think I hear "Old Time's Sake," not "Old Kindness' Sake." I don't hear the extra syllable needed to make "time's sake" into "kindness' sake."

I did find one set of lyrics on the web, at http://www.jiva.co.uk/songs/notelling.htm
and they have it "Old Times' Sake." So it's still a toss-up.

So, since there are so many versions, I'm going to sing what I want, which is "Old Time Parade." I know it's not what she sings -- that "k" sound is definitely not a "d" sound -- but it rhymes with the proper word in the last line of the stanza.

By the way, I note that the song uses an interesting rhyme scheme; ABCB for the first four lines, then DDDE for the last four. Exquisite.

Bob