My family history is from the South too. I do what my Mom and Grandmother did up to a point. One thing I have learned is that gravy will be much more flavorful if no water is added in the final preparation. Different meats drippings get different treatment. For turkey gravy I drain the liquid after baking it and put in a fat separator. One thing I do that might be different is I brown my flour till it is a light tan color in a dry skillet over med high heat, constantly scraping or stirring it off the bottom to keep it from burning. Once it is the right color I take it off, cool it then sift and store it for future use. So when I make turkey gravy I use part browned flour and part cornstarch mixed with enough turkey liquid to make it runny then back into the pan with the rest of the liquid. And I do use a whisk. I would be lost without the whisk.
Heat it till thickened and boils. I use just the browned flour for beef gravy. If the liquid needs salt I use a small amount of chicken base or beef base so the flavor is intensified. I always save the liquid from crockpot beef and chicken and it makes wonderful flavored liquid to use for such purposes. Good Gravy !!