Cut 4 large squares of aluminum foil. Place 2 slices of bread side-by-side on each piece of foil. Spread the bread slices with Thousand Island dressing. Evenly divide the corned beef, Swiss cheese, and sauerkraut among the bread. Top with a second slice of bread to make a sandwich. Wrap the foil snugly around the sandwich to make a sealed packet.
Place the packets on the preheated grill. Cook, turning every 10 minutes, until the bread is lightly toasted and cheese melted, about 30 minutes.