Preheat oven to 350°F. Spread cornbread onto two baking sheets lined with parchment. Bake until golden, 15 to 20 minutes. Transfer to a bowl. (Keep oven on.)
Heat oil over medium-high in an ovenproof skillet. Cook sausage, breaking it up with a spoon, until cooked through, 8 to 10 minutes. Transfer to bowl with cornbread, leaving oil in pan.
Add onions, celery, salt, and pepper to skillet and cook over medium, stirring often, 10 to 12 minutes. Add garlic and sage and cook, stirring occasionally, until fragrant, 2 minutes. Transfer onion mixture to cornbread mixture. Add parsley and pecans.
In same skillet, heat vinegar over medium heat and deglaze pan, scraping up browned bits as mixture boils, until most liquid has evaporated, about 30 seconds. Add 6 Tbs. butter to skillet, stirring often, until melted, 3 minutes. Drizzle vinegar mixture over cornbread mixture. Set skillet aside.
Whisk eggs and 1 1/2 cups stock in a bowl; pour over cornbread mixture. Gently toss, adding more stock, 2 Tbs. at a time, as needed, until cornbread is hydrated. Transfer back to skillet. Cut the remaining 2 Tbs. butter into cubes and sprinkle over cornbread mixture. Cover with buttered foil and bake until a knife inserted into center comes out hot, 30 to 35 minutes. Remove from oven and uncover. Increase oven temperature to 425°F. Bake until golden, 20 to 25 minutes. Let stuffing rest for 10 minutes.