I believe Cheer, boys, cheer has also been used for a gold mining song in NZ but I haven't managed to find it.
I did, however, find a political version in Bailey and Roth's 'Shanties by the way', dated 1858.

Cheer, boys, cheer, the polling day's before us,
Head of the poll we'll have our hero brave,
Onward, brave hearts, to victory attaining;
Where is the man that would be a Wakefield slave?

There were 3 other verses but the chorus for this one is:

Cheer, boys, cheer, we'll crush the Wakefield faction,
Cheer, boys, cheer, the craven rads shall run,
Cheer, boys, cheer, the little Saint we'll spurn, boys,
Cheers, boys, cheer, for gallant Featherston.

However, the other faction also used the same song with different words - their chorus went:

Cheer, boys, cheer, a fig for frown or favour,
Fear no more the greedy crew that storm;
Cheer, boys, cheer, we will have land for labour;
Cheer, boys, cheer! for RADICAL REFORM!


It was an election for Superintendent of the Wellington Province and Ashton St Hill was opposing Isaac Featherston. (Featherston won the election.)
But obviously it was a song that was well known in NZ, not long after Sebastopol and before the Civil War.
Robyn