How did the term shit-eating grin come about? I’m aware this might not have a specific answer but I just don’t get how eating a turd would make you smile in a fake way.
I believe it’s a reference to the kind of frozen smile you’d have on your face when you’ve been caught eating shit (or doing anything else that you’re embarrassed to be caught doing).
Caution: this was asked and never answered more than ten years ago.
But yeah, I’d bet it comes down to more “big rueful grin” than “cat who ate the canary grin.” The latter meaning seems to have pushed out the original, as I can only think of usages that conform to being very pleased with yourself.
I will forever associate a “shit-eating grin” with a shit-eating Divine (SFW) in Pink Flamingos.
ETA: Ninja-ed in the linked thread.
Hm, I thought the implication was that the person grinning is stupid–so stupid that he grins like an idiot who doesn’t understand that shit is disgusting.
I assume a shit-eating grin is what is being illustrated by Slug Signorino here.
What the OED has to say
This is closer to the connotation in every case where I’ve ever heard it used. It’s a grin that is smug, totally self-satisfied, and foolish. It’s a “foolish grin.”
It’s the sort of grin that makes you want to go up to the guy and yell “Eat shit” at him, to wipe the damn thing off his face.
Kinda my impression as well. I imagine a wide-eyed stare along with the grin.
I doubt this is the origin, but whenever I hear the expression I think of a dog who’s found the litter box.
Asked twice by me (once as a topic and once in another topic) if you want to read past replies. Both times had a few answers.
OED cite for 2009. Presumably on-line–I didn’t know that it thus has a variable cut-off date for citations.
Coprophagia has been around for a long time. For recent examples check your local Internet.
I always thought something like that was the origin. I’ve seen the shit eating grin on dogs.
I have always used it as definition “a.,” but on these boards, I encounter definition “b.” quite a bit.
Nicely put, I don’t mean that in a brown nosing way. 
I’ve always associated it with children. They get caught doing something they know is wrong (like eating shit - kids literally put everything in their mouths), but try to deflect punishment by both looking as cute as possible and illustrating how happy their bad choice has made them.
There’s also the related (I assume) phrase ‘Grinned like a fox eating shit off a (wire) brush’ which I first encountered in Merlin by Robert Nye.
My image of both phrases is of someone gingerly touching a turd to their teeth, while desparately trying to keep their lips away from it. Not actually a grin, but a weird expression a bit like an extreme one.
It originated with Robert Nye (he’s brilliant - try to read some of his stuff) not sure if it was Merlin or Faust - when he repeatedly says the phrase “…and he grinned. He grinned like a fox eating shit out of a wire brush” - it had never been done prior to this. The next time I heard it was on TV about 25 years later. The book was from late 70s I think. It has been copied many many times since and no-one has the grace to give credit to a fantastic and image-full writing. You can imagine the grin !
It goes back MUCH farther than that. It was a commonly used phrase when I was serving in the U.S. Navy in the early '70s, and had been in common use there for a great many years before that.