Remove the wrapping, and place the giblets and turkey neck into a large saucepan with onion, celery, white pepper, and turkey gravy mix. Pour the chicken broth over the mixture, bring to a simmer over medium-low heat, and simmer for 30 minutes. Remove the turkey liver and set aside. Allow the stock to simmer for 2 1/2 more hours. Stock should equal about 3 cups; add more chicken broth if necessary. Remove the giblets and chop them if you want to put them back into the gravy. Chop the liver if desired. Strain the stock into a saucepan; discard bones and spent vegetables.
When the turkey is finished roasting, pour the drippings into a fat separator or bowl, and skim off the fat. In a bowl, whisk the quick-mixing flour with the pan drippings until smooth, then whisk the flour mixture into the stock. Bring the gravy mixture to a simmer over medium heat, whisking constantly, and add the chopped giblets, if desired.