I always heard “another thing coming” until sometime in, say, the last twenty years. I took “another think coming” to be a variant people employed to be funny. Since I am not much younger than Rand Simberg, it may have once been a regionalism to use think rather than thing, so we learned it differently when young. It’s unfortunate that noting the difference was lent emotional attachment by deploying it as Sarah-bashing, thinking she’s stupid for using the more common version of a phrase.
On the plus side, from the comment thread I learned that “another think coming” was the original, largely replaced by morphing of the language.