Agree -- nutcakes your method is better than what I suggested.

Mix a couple Tbsp of fat drippings with a couple Tbsp flour in a pan and cook to loose the raw flour taste. Then add any turkey juices mixed with chicken stock and bring to a simmer. Simmer till thickened. You can further thicken using flour mashed with butter and add a bit at a time. Some people do just add the flour mixed in with water, but it tastes a little raw.

If you thicken with flour, yes mix with water or broth first before whisking this mixture into the pan drippings. Personally I say no thickener -- add wine, sherry or brandy to the pan drippings, to scrape them up. Then add some herbs and broth and reduce until concentrated. Swirl in a tablespoon or two of butter if feeling decadent.