Wrap and refrigerate liver until needed. In a medium saucepan combine remaining giblets, neck, celery, onion, 2-1/2 cups water, and the first 1/4 teaspoon salt. Bring to boiling; reduce heat. Cover and simmer about 1 hour or until tender. Add chilled liver; simmer 20 to 30 minutes more for turkey (5 to 10 minutes more for chicken) or until tender. Remove neck and giblets from broth. Discard neck; finely chop giblets. Strain broth, discarding vegetables. Cover and chill giblets and broth until needed.
After transferring roasted turkey or chicken to a serving platter, pour pan drippings into a large glass measuring cup. Skim and reserve 1/4 cup of the fat from drippings. Transfer the 1/4 cup fat to a medium saucepan and set aside. (Discard any remaining fat.)
Measure the remaining poultry juices; add reserved giblet broth as needed to equal 2-1/2 cups total liquid.
Stir flour, pepper, and remaining 1/4 teaspoon salt into fat in saucepan until completely smooth (there should be no flecks of flour). Pour the broth mixture all at once into the flour mixture. Stir in sage or thyme and garlic.
Cook and stir over medium heat until thickened and bubbly. Cook and stir for 1 minute more. Stir in chopped giblets and a few drops of Kitchen Bouquet, if desired. Makes 3 cups (10 to 12 servings).