Prepare the Thousand Island Dressing: Combine the mayo, ketchup, vinegar, sugar, relish, onion and salt and pepper in a small mixing bowl. Transfer to a small container and chill until ready to use.
Prepare the sandwiches: Lay out all of the pieces of bread into pairs. Add a layer of the prepared Thousand Island dressing onto each slice. Top one piece of bread with cheese and the other with pastrami. Add a spoonful of sauerkraut on top of the cheese. Keeping the sauerkraut in the middle will help the bread to not get soggy.
Bring both sides together to form your sandwich. Add a layer of butter to the outside of each piece of bread and grill until cheese has melted and everything is warmed through.