Prepare the Signature Sauce:

1. In a small bowl, combine the mayonnaise, ketchup, sweet pickle relish, chopped onion, white vinegar, Worcestershire sauce, paprika, garlic powder, pickle juice, horseradish, salt, and pepper.
2. Mix well until all ingredients are fully incorporated. Adjust seasoning to taste.

Assemble the Sandwiches:

1. Spread a generous amount of the Signature Sauce onto one side of each slice of marbled rye bread.
2. Layer the corned beef evenly on top of the Signature Sauce on 4 slices of bread.
3. Top the corned beef with sauerkraut, dividing it evenly among the sandwiches.
4. Place 2 slices of Swiss cheese on top of the sauerkraut on each sandwich.
5. Top each sandwich with another slice of marbled rye bread, Signature Sauce side down.

Grill the Sandwiches:

1. Heat a large skillet or griddle over medium heat and add a little butter.
2. Once the butter is melted and the skillet is hot, carefully transfer the assembled sandwiches to the skillet.
3. Cook the sandwiches for 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
4. Press down gently on the sandwiches with a spatula while cooking to help them crisp up and melt the cheese evenly.

Serve:

1. Remove the sandwiches from the skillet and transfer them to a cutting board.
2. Use a sharp knife to slice each sandwich in half diagonally.