Never had a hot dog at an A&W, just hamburgers and, of course, root beer, but in Buffalo, there's a little place called Ted's Charcoal Hots that has fantastic hot suace. Here is a recipe for a reasonable facsimilie of their sauce:
TED’S HOT DOG SAUCE
1 1/2 teaspoons olive oil
1 small onion, dliced
1 red bell pepper, diced
4 cups water
1 tablespoon tomato paste
2 teaspoons corn syrup
1 teaspoon cornstarch
1/2 teaspoon salt
1 teaspoon crushed red pepper
1 tablespoon chile powder
1 teaspoon paprika
1/4 cup vinegar
1 10-oz jar sweet pickle relish
Heat the oil in a large saucepan over medium heat. Sauté diced onion and bell pepper in the oil for 5 minutes, until onions are soft but not brown. Add water, tomato paste, corn syrup, cornstarch, salt, and red pepper flakes, and stir. Bring mixture to a boil, then reduce heat and simmer for 30 minutes. Add vinegar. Continue to simmer for an additiona1 30 minutes or until most of the liquid has reduced and the sauce is thick. Add relish and stir to heat through, then turn OFF burner.