Right now the only example for this is “But Tidy hinched, and Tidy flinched,” from "Children's Literature A Textbook of Sources for Teachers and Teacher-Training Classes." I think it's from a song about an old man in the woods--a song which is called, variously, "Father Grumble," or "John Grumble," or "Equinoctial and Phoebe," or (my favorite) "The Old Man in the Wood." I love Jean Ritchie's version--when she sings about the old man's attempts to milk the cow, she tells us "Tiny hitched and Tiny flitched." But in someone else's version over here, "Tiny hitched and Tiny twitched," and over here, "Tiny hinched and Tiny flinched."
The Century's definition for hinch is "To be stingy; be miserly; grudge." I've known some cows like that--but I've never heard anyone call a cow "Tidy."