In a small bowl mix the mayonnaise, grated onion, ketchup, sweet pickle relish, paprika, and salt together.
Place a piece of Swiss cheese on each slice of bread. Spread about 1 tablespoon of dressing over each slice of bread.
Add the corned beef to four of those slices of bread, dividing evenly. Add the sauerkraut to the other four slices of bread, dividing evenly. Carefully fold the corned beef sides onto sauerkraut sides to form 4 sandwiches.
Spread soft butter over the top of each sandwich. Place the sandwich butter side down in a hot skillet over medium-low heat. Spread butter over the side facing up. Cover the skillet loosely with aluminum foil. Cook until the bottom is golden brown then flip.
Cover and cook until the other side is golden brown. The sandwich should be heated through and the cheese should be melted.