Updated 3 May 2012:
So I finally created a very close clone.
1/2 cup Hellman’s mayonnaise3 tablespoons creamy French dressing (wishbone deluxe)4 teaspoons sweet pickle relish4 teaspoons dill pickle relish1 tablespoon finely minced white onion (or grated white onion on microplane grater)1 teaspoon white vinegar1 teaspoon sugar1/8 teaspoon salt1/4 teaspoon marmite
mix and let chill for 4 hours or more. Just in time for 2012 Point to Point

One I’ve been using a while:

• 1 teaspoon onion grated on a microplane grater
• 1 1/2 tablespoons mayonnaise
• 1 1/2 teaspoons sweet pickle relish
• 1 teaspoon yellow mustard
• 1 teaspoon sugar
• 1/4 teaspoon marmite
• 1/4 teaspoon ground turmeric

combine and refrigerate for more than an hour.Or this one:
1/2 cup mayonnaise or Miracle Whip(ugh!)
2 tablespoons French dressing
4 teaspoons sweet pickle relish
1 tablespoon finely minced white onion
1 teaspoon white vinegar
1 teaspoon sugar
1/8 teaspoon salt

another vote for:
1/2 cup mayonnaise
2 tablespoons French dressing
4 teaspoons sweet pickle relish
1 tablespoon finely minced white onion
1 teaspoon white vinegar
1 teaspoon sugar
1/8 teaspoon salt
1. Combine all of the ingredients in a small bowl. Stir well.
2. Place sauce in a covered container and refrigerate for several hours, or overnight, so that the flavors blend. Stir the sauce a couple of times as it chills.

Makes about 3/4 cup.
or this one:
1/4 Cup Mayonnaise
2 Tablespoons Catalina Salad Dressing (recipe here)
1 Tablespoon diced Dill Pickle
2 teaspoons Dill Pickle Juice
Directions:
Combine the mayonnaise, Catalina dressing, pickles, and pickle juice in a small bowl.

and another vote

• 1 cup miracle whip
• 1/3 cup sweet relish
• 1/4 cup french dressing
• 1 tablespoon sugar
• 1/4 teaspoon black pepper
• 1 teaspoon minced onion

but then I found this recipe:
This “top-secret recipe” is from a McDonalds Manager’s Handbook published in 1969. It was meant to be used only as an emergency recipe for stores that ran out of the pre-made sauce that each store used on the Big Macs®. But, this page in the handbook was quickly removed for fear of other burger chains learning and using the top-secret sauce. But, it was too late. The recipe somehow got out and was made public the next year, and has been available ever since.

Yields: 1 cup, or enough for 8 burgers

Prep Time: 10 minutes

Cook Time: 1 minute

Total Time: 11 minutes

Ingredients:

• 1/4 cup salad dressing (like Miracle Whip®)
• 1/4 cup mayonnaise
• 3 tbsp French salad dressing
• 1/2 tbsp sweet pickle relish
• 1 1/2 tbsp dill pickle relish
• 1 tsp sugar
• 1 tsp dried, minced onion
• 1 tsp white vinegar
• 1 tsp ketchup
• 1/8 tsp salt

Preparation:

 

1. Mix all ingredients, and stir well in a small container.
2. Microwave on high for 25 seconds, and stir well again.
3. Cover, and refrigerate at least 1 hour before serving.

Or this one:

1/2 cup mayonnaise

2 tablespoons French dressing

4 teaspoons sweet pickle relish

1 tablespoon finely minced white onion

1 teaspoon white vinegar

1 teaspoon sugar

1/8 teaspoon salt