Perhaps this song from 1861 inspired Galusha's. Ye olde Folk process.

It too is about the Irish at Bull Run; the attitude and the meter are right, and it has the somewhat unusual characteristic of an internal rhyme in several fourth lines. Four of those fourth lines (including the memorably colloquial finale) end in the phrase "the battle of Bull Run":

                         BATTLE OF BULL RUN.

Our gallant soldiers they are going to leave their friends to mourn.
To watch and pray both night and day their quick and safe return.
We are going to face the enemy and put rebellion down,
May we return victoriously and wear a laurel crown.

Our gallant soldiers they are going to fight a glorious cause,
To defend the Flag and Union, the Government and its Laws.
Kind fortune smile upon our brow wherever we may go,
We will never yield upon the field to any mortal foe.

Our gallant soldiers, they are going to the battle-field of fame.
To defend the glorious stars and stripes and put to flight with shame.
Each proud secession leader, with bayonet, sword and gun,
And to make him pay severely for the battle of Bull Run.

The gallant Fire Zouaves they fought like lions brave,
Likewise the Massachusetts boys most manfully behaved;
The gallant 27th their foes they did not shun,
But the glorious 69th, was the terror of Bull Run.

Long life to Gen. Meagher, that Irish blood of fame,
Who wore the harp and shamrock upon the battle plain;
Who, said unto his gallant men, "remember Fontenoy,"
Then the whole at large with bayonets charged, their foes they did
deploy.

When the gallant Col. Corcoran lay prostrate on the ground,
Weary and fatigued, and exhausted from his wounds,
He said unto his gallant men, brave boys I am not undone.
We will make them pay some other day for the battle of Bull Run.

Over ten long hours we had fought against an enemy,
Of four to one a fearful odds of men, we could not see.
Until among our teamsters a panie had begun,
Then we did retreat but were not beat at the battle of Bull Run.

A. W. AUNER, SONG PUBLISHER, 110 N. 10th St., ab Arch, Philadelphia.