I learned that Nyth a Gwcw from two Welsh musicians, but they called it Nyth a Gog. The B part of Nyth a Gwcw shares a few measures with the A part of Jacky Tar, but I think they are different enough to be considered two different tunes.

For those not familiar with Welsh, w can sound like u, so that Gwcw is pronounced goocoo - obviously cuckoo.

I enjoyed your rendition of Jacky Tar, Mr. Happy.