I was curious to see if there were any developments on this thread since my first post 4 years ago... Thanks for all the contributions.

I wish to apologise for my earlier half-baked "Polish Whaling Song" reference, and correct my assertion that the Behan brothers were inspired by the tune of a Polish whaling song for "The Ould Triangle". Here is the source of my confusion:

https://www.youtube.com/watch?v=0mEoMCp-o1g

However, as can be seen from the comment by William Strauss, the lyrics were actually written in recent times by Bogdan Kuśka (of the Polish group, "Ryczące Dwudziestki"); it is probably safer to assume (until someone with better Polish than mine can confirm otherwise!) that the Dubliners' performance of "The Ould Triangle" probably inspired the performers in the Youtube video ("Mlynn"), but that's only conjecture.

Nevertheless, although we can probably safely dismiss the idea of Polish inspiration, Tom Neary elsewhere on Mudcat ( thread.cfm?threadid=22222#2905615 )
gives us good reason to believe that Brendan Behan's friend, Dicky Shannon in fact wrote The Old/Ould/Auld Triangle. (Based on the air of "The Galway Shawl".)

Sorry for any confusion and thanks again to everyone for their help with "Willie Gannon".

Ray