'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":
Here is how you do it [leave a work party early]: Do not tell anyone you're leaving. No one needs to know you're heading out. Because no one cares. Don't say good-bye. Don't make a big deal about it. Just go. Don't go over there and say bye to your boss. You talked to your boss when you got here. Does he look like he wants to hear from you right now? So go.
This is the Irish Exit. The Irish Exit involves simply leaving without saying good-bye. It's unclear why this is referred to as the Irish Exit. Because in Ireland, people love saying good-bye. It's an art form. Thus, good-byes can take forever. The Irish Exit may be the result of Irish people trying to avoid the 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:
I recently learned that an “Irish exit” is when you leave I a party without telling anyone (and presumably it is because you are too drunk to form words).
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":
So in closing, I'd like to pay tribute to the introverts' secret weapon—one of our greatest coping mechanisms for handling social situations. The Irish goodbye is something I've perfected over the years. No offense to the Irish with that term. You guys are geniuses for coming up with this patented method of getting the hell out of Dodge without having to explain why. Even if I'm drunk, I can slip out of any event, very subtle and ninjalike, and with no warning—a classic introvert move I rely upon heavily. I'm like Omar from The Wire. Except no.
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]:
Hail and farewell, America. It was unlikely he would ever walk the streets of her cities again; so an Irish blessing and an Irish goodbye to America's people who shall never have an ending, never have an ending, never have an ending.
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):
We had been drinking all night at our favorite local bar and I pulled my usual leave-without-saying-goodbye move. The good old Irish goodbye. About an hour later, they found me asleep in a vegetable stand across the street from our apartment. My roommates had to literally pick me up and carry me home.
And from Donncha O'Callaghan, Joking Apart: My Autobiography (2011):
Among the South Africans and New Zealanders that played with Munster [an Irish rugby union team] I noticed the same expectations: all of them were liable to greet you in the morning with high fives and good humour and expected a similar greeting in return. It probably exposes our reticence as a people. We're not good t warm greetings or goodbyes. Finbar Quaid, a friend of mine who spent some time living in Argentina, says that the locals over there call it 'The Irish Goodbye'. At the end of the night, when we've had enough. we're liable just to slip away without a word.
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).
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.