Urban Dictionary gives two almost opposite meanings of Irish goodbye
Leaving quietly out the side door of a party or bar without saying
goodbye to anyone. Mostly due to the fact that family or friends would
most likely take your keys away for being to intoxicated.next morning:
Irish goodbye O'leary? You should not have been driving!
versus
A goodbye taking more than 1 hour and in which a new conversation begins. People can spend hours on end standing in the driveway talking, during an Irish Goodbye. Not limited to Irish people, but very common among large Irish Families.
This type of goodbye is different because the more serious one is about leaving, the longer they stay around for.
T: Im going to bed for real
H: Okay goodnight
T: Wait, did you hear the new ___ album yet?
H: Yes, wasnt it amazing??
T: Most awesome of all time because…3 hours later
T: Okay this Irish Goodbye must come to an end. I'm going to just hang up the phone otherwise we'll never stop talking.
I can find an example of the first meaning (leaving suddenly without telling anyone), for example in What you need to know about the Irish Goodbye this Christmas party season, but I can't find examples of the latter meaning being used, even though that's the meaning I previously associated with the term.
Oddly enough, I can't find the phrase in Google NGrams.
Related question, with an answer mentioning "Irish goodbye" but citing Urban Dictionary: Is there an English phrase for an inability to actually *leave* already?
Best Answer
'Irish goodbye' or 'Irish exit'—or either one?
Ross McCammon, Works Well with Others: An Outsider's Guide to Shaking Hands, Shutting Up, and Other Crucial Skills in Business That No One Ever Teaches You (2015) takes the position that the discreet departure is more accurately termed an "Irish Exit" and in fact is the opposite of the endless "Irish Goodbye":
Mindy Kaling, Is Everyone Hanging Out Without Me? (And Other Concerns) (2011) likewise uses the wording "Irish exit" for silent departure from a gathering:
But she doesn't discuss "Irish goodbye" at all, so we don't know whether she is using "Irish exit" as a variant of "Irish goodbye" or as a separate thing. The way Ross McCannon does. Who is in fact the only author in my Google Books search results who does. Which makes me doubt that he is trustworthy on this point. No matter how definitive his clipped sentence fragments seem.
On the other hand, Amy Schumer, The Girl with the Lower Back Tattoo (2016) favors "Irish goodbye" for "quiet getaway" and ignores "Irish exit":
The other sources I checked that use "Irish goodbye" adopt Schumer's meaning as well.
A look at the earliest Google Books occurrences of this slang expression
Sean O'Casey, Mirror in My House: The Autobiography of Sean O'Casey (1954) has a sincere farewell, not a sneakaway, in mind in this excerpt [combined snippets]:
Note that it is the American people, not the Irish goodbye, that "shall never have an ending." I see no hint here that O'Casey was conversant with the notion of "Irish goodbye" as a slang term for slipping away undetected.
The earliest Google Books matches I could find for "Irish Goodbye" in a nonliteral, slangy sense are two from 2011. From Mark Rosenberg, Blackouts and Breakdowns (2011):
And from Donncha O'Callaghan, Joking Apart: My Autobiography (2011):
The earliest corresponding matches for "Irish exit" are also from 2011—Kaling's (cited above) and a mention in the acknowledgments to Gregg Seidl, Wicked New Albany (2011) of the proprietor of a bar or eatery in New Albany, Indiana, called The Irish Exit (possibly an allusion to people leaving without paying, in which case the ethnic focus of the expression acquires a rather pejorative edge).
Conclusion
None of the slang dictionaries I consulted have a listing for either "Irish goodbye" or "Irish exit," from which I conclude that it's a fairly new term. Relative newness is of course an invitation to confusion over what the term means; but the vast majority of instances of both "Irish goodbye" and Irish exit" use it in the sense of "departure without taking leave"—and once that meaning catches hold, it's hard to see why anyone would want to push for a contrary meaning along the lines of "interminable emotional leave taking."
The vast majority of Google Books matches for both "Irish goodbye" and "Irish exit" use the terms in their shared "slip away unnoticed" sense. That appears to be the terms' primary meaning today, and I expect that it will also be their long-term meaning, if either or both prove to have staying power as slang.