Preheat a panini grill. OR, heat a grill pan or cast-iron skillet over medium heat.
Make the sauce by combining the ketchup, mayonnaise, sweet relish, and dried mustard in a dish; mix until well combined.
Prepare the sandwich by slathering a piece of rye bread with some of the sauce, then top with pastrami, well-drained sauerkraut, and Swiss cheese. Add more sauce to the remaining piece of bread, if desired, then place it on top of the sandwich.
Cook the sandwich by placing it on the preheated panini maker and cooking for 5 minutes or until golden brown and crunchy.
For the stovetop, cook the sandwich in a grill pan or cast-iron skillet over medium heat for a few minutes on each side until golden brown, warmed through, and the cheese is gooey. Side Note: I don't add butter to the bread before cooking, but feel free to do so if you prefer.