Green’s Dictionary of Slang says this term for “idiot” is “usually Irish.” Green’s gives quite a few alternative spellings — “edgit, eedjit, eegot, eejut, e-jit, ejot, idjeet, idjet, idjit, idjut, ijet, ijit, ijjit, ijiot, ijut” — which complicates the nationality issue, since Green has found “idjut,” “idjit,” “idjet,” and “ijit” in U.S. sources from the 1880s through the twentieth century.
But not “eejit,” which, I’m pretty sure, is a separate thing. Over at Urban Dictionary, some commenters say it’s Scottish as well as Irish; others say that is shite. A couple of them suggest that calling someone an eejit is less harsh than calling them an idiot.
“Eejit” first pops up in a New Zealand newspaper in 1899:

Green’s first Irish sighting is from a 1929 book: “A big eejit of a bobby is after takin’ her to College Street Station.” Since then it’s been common in Ireland, and is frequently used by the characters in Brian Friel’s plays. More recently, Cillian Murphy, the star of Oppenheimer, reflecting on celebrity, said “You’d be an eejit not to enjoy it.”
As for American use, it’s admittedly sparse. In 2017, prizefighter Floyd Mayweather unleashed it on Conor McGregor while in Toronto promoting their upcoming fight.

In 2013, a New York Times reviewer paraphrased Scott McCracken’s memoir Crapalachia: “In other words, we aren’t the eejits; y’all are.”
Not surprisingly, given his fondness for “fecking” and “gobshite,” the heaviest American user is journalist Charles Pierce. Here’s a sampling of some of his Twitter/X posts:

I wouldn’t be surprised if “eejit” catches on. It’s pungent and fun to say, and there sure are a lot of them out there.

I used the word recently, for the first time in many years. On a walking tour of Nice, I asked a chummy rugger bugger the Irish word for ‘lout’. He was stumped for a few seconds, so I suggested ‘eejit’. He finally decided his word for ‘lout’ was ‘lout’.
He wasn’t a rugger bugger in the English sense, and perhaps not even in the Irish. I mainly wanted to type rugger bugger. There, I’ve done it again!