I have never heard this particular song by Bob Gibson. I stumbled across this looking for lyrics to his Ski Songs album. However there is another song that mentions Lincoln asking the band to play "Dixie". It is the Johnny Horton song "Johnny Reb".

When, "Honest Abe", heard the news about your fall
The folks thought he'd call a great victory ball
But he asked the band to play the song, Dixie
For you Johnny Reb and all that you believed