Rollo Treadway wrote:When Chaplin wrote the music for his 1942 re-release of
The Gold Rush, I'm pretty sure that "Sing a Song", the little ditty written for the original release, fell by the wayside.

I think we knew for sure that "Sing a Song" was not used in the 1942 score for THE GOLD RUSH, but just because I have it right here and can check it easily, I thought I'd take a look at the Music Cue Sheet for the 1942 scored version (dated May 8, 1942) and see if "Sing a Song" is listed.
Sure enough it's not.
But there's some other interesting things we can see about the 1942 score.
There are 99 cues used in the movie but only two that are actually written by Chaplin by himself (entitled "Leaps and Creeps" and "Leaps"). All the other Chaplin composer credits are in conjunction with Max Terr. And there are a actually several that were not written by Chaplin at all: some are by Terr by himself. And some by Gerard Carbonara, and some credited to Carbonara and Terr together.
Also included is one selection by Archibald Joyce ("A Thousand Kisses", played twice) and one number credited to Louis Bourgeois, arranged by Max Terr. There are some classical oldies (by Brahms, Rimsky-Korsakov, Wagner, Tchaikovsky and Rossini), used. Some of those are credited as Arranged by Chaplin and Terr, and some by Terr without Chaplin.
And, just to cover them all: the performance of "Auld Lang Syne" (cue #66) has no writer or arranger credit at all.