Bring a large pot of salted water to a rolling boil. Add the elbow pasta and cook until fully tender, approximately 7 to 9 minutes. Drain thoroughly and rinse under cold water to halt cooking. Set aside to cool completely.
In a sizable bowl, combine the mayonnaise, yellow mustard, sugar, white vinegar, salt, black pepper, and sweet relish. Whisk until the mixture becomes smooth and homogeneous.
To the prepared dressing, add the cooled pasta, chopped hard-boiled eggs, minced celery, diced onion, and optional red bell pepper. Using a large spoon or spatula, fold the ingredients together delicately until every element is evenly coated.
Cover the bowl with a lid or plastic wrap and place it in the refrigerator for a minimum of 2 hours to allow the flavors to meld. Stir gently before presenting for service.