A composition by Brendan Mulvihill (I hope he doesn’t mind me posting it). I transcribed it from his playing where he pairs it with Cock and the Hen:
(My version of it in the comments.)
Both tunes have a nice non-symmetrical rhythm to them; I think of them as anti-slip-jig slip jigs. Quite a good set!
So this was named in honor of fiddle player Eugene O’Donnell, was it?
I don’t know for sure, but it’s likely…there are a few tunes named for him.