Also, in case the Irish thing misleads, o’ as a contraction of “of” isn’t necessarily Irish: in Irish names, O’ means “son of” (there’s a recent thread somewhere where I posted an incorrect derivation and someone corrected me, but I can’t search for it for obvious reasons).
David J. Skal in Death Makes a Holiday (2002) says that though it is often claimed that hollowed turnips with candles in them were part of a traditional celebration of Halloween in the British Isles, there is little documentary evidence for the notion.
Nicholas Rogers in Halloween (2002) quotes a Canadian newspaper’s 1866 description of a carved illuminated pumpkin made on Halloween, but it doesn’t use the word jack o’ lantern: “There was a great sacrific of pumpkins from which to make transparent heads and face, lighted up by the unfailing two inches of tallow candle.”
W.B. Yeats published a collection of Irish fairy and folktales that had a story similar to that summarised by the wiki, but it didn’t have a jack o’lantern in it. Instead, the protagnist is named Billy Dawson. When Old Nick refuses Billy entry to Hell, he tweaks Billy’s nose and sets it on fire, because of all the alcohol Billy has drunk in his lifetime. Since Billy’s also been turned away from Heaven, he’s doomed to wander the earth, with his flaming nose, so he becomse “Will o’the Wisp”.