As I mentioned, the phrase was common and lots of songs included it; we don't need to list them. Jimmy mentions one such (the same song that Tim guessed at, as it happens) which Kearney seems to have written using the Scottish song as a rough model. It is not otherwise related to it, though, and is irrelevant to this discussion except as a footnote (which we now have, so there is no need to repeat). Both songs are already in the DT and have been discussed here before.

ERIN-GO-BRAGH  (reasonably accurate transcription, presumably from the Gaughan record)

ERIN GO BRAGH  (Peadar Kearney; source not named)

The story is always the same; "versions" don't differ very much and all derive from the broadside texts. The Highlander is not mistaken for an Irish "rebel", but for a petty criminal. Let's not romanticise unduly. The song does make a good point about cultural assumptions and prejudice (it won't have been uncommon for Highlanders to be mistaken -prejudicially- for Irish at that time in quite large parts of Scotland, and the "Highlander in the big city" joke was far from new) but it's a modest enough point, on the lines of "No, I'm not; but some of my best friends are".