Prepare the sauce by combining the mayonnaise, ketchup, and sweet pickle relish in a small bowl. Mix well.
Make the sliders by spreading a bit of the sauce on each slice of cocktail rye bread.
Layer one slice of bread with pastrami, then a bit of sauerkraut, then top with Swiss cheese, and the other slice of bread.
Cook the sliders by heating a large skillet over medium heat, then add the sandwiches. Cook for 3-4 minutes or until crisp and golden brown, then flip and cook for 2-3 minutes.