What a fun discussion. Kathleen is not an Irish song but Irish people love it. SO do many Italians, Germans, and other Mutts here in Central New York. The nicest version I have heard of it was in Rio Grande as sung by The Sons of the Pioneers.

Immigrant Eyes is the most often requested song on two local radio shows. The Italian Hour and The Irish Radio Show both on WDWN FM 88.9.
The song mentions neither country or where Grandfather came from but it speaks to all immigrants. The Irish seem to think it's theirs but I doubt Guy Clark cares.

Belfast Mill isn't about Belfast and it is actually called Aragon Mill. A mill that isn't in Ireland.    A little poetic license and the song is Irish. I wonder how Si Kahn sorts out the royalties?

Don