Hi Stella :-) While this recipe may not be the Brinkmann recipe, it sounds close (It has the ingredients in it that you listed.). Let me know if this sounds familiar. I do hope it is the one you are looking for.

Chinese Barbeque Sauce

3/4 cup catsup
3 tbsp soy sauce
1 tbsp liquid smoke
1/2 cup brown sugar
1 tbsp ground ginger
2 cloves garlic, minced

Combine all ingredients and heat until sugar is dissolved and bubbly.

Chinese Smokey Ribs
Yield: 6 servings

6 lb Pork spareribs
Chinese dry marinade

Rub ribs thoroughly with the Chinese Dry Marinade. Let stand at room temperature for 1 to 2 hours.

Arrange ribs ends down on cooking grill or place bones upright in rib rack.

Smoke-cook until done. Brush ribs with Chinese Barbecue sauce during the last few minutes of cooking, then serve with remaining sauce.