He grew whiskers on his chinnigan
The wind came along and blew them in again
Poor old Michael Finnigan, begin again.
What is that tune!?
It's the same tune at the start of "Way Down Yonder in the Paw-Paw Patch" which I realize many people won't know (and which has a fancier fourth line, musically).
And Raffi sings "Bumpin' up and down in my little red wagon" to that tune with an ending kind of like Michael Finnigan's, without the endless repeats.
And "one little, two little, three little Indians" which isn't politically correct (and has yet a different little end tune).
Some fiddler or concertina player might know the generic tune-name, or older songs with that tune. I might know older songs but it's so common it's in my little-kid brain, not my adult musician brain, like the tune to the ABCs and Twinkle, twinkle little star, which many people don't realize are the same tune for years (and some will realize it when they read this). Baa baa black sheep.