It'd be better to cook a BBQ sauce in large quantity on a day you cook some pork conventionally and freeze it for later for sous-vide pulled-pork.

One recipe I like serves first as cooking liquid for ribs, then it's reduced over high heat (for quite a while) until syrupy consistency (more or less, to taste). The ingredients are japanese (it comes from a japanese recipe for American style BBQ...), but it's pretty related to the more traditional American BBQ sauces in the end, and tastes similar.

• Classic brunoise (equal parts of chopped leeks, carrots, celery), well browned.
• Water enough to cover the ribs (usually quite a few liters as I do big batches)
• Tomato paste (a few generous squeezes, or a small can)
• Brown sugar or maple syrup to taste.
• Mirin, a few spoons
• A cup or two of saké (works just as well with beer)
• Shoyu (Chinese soy sauce works too)
• an head of garlic, just the top removed.
• a few stars of anise
• a generous knob of ginger.
• rice or apple cider vinegar
• A few spoons of miso, which adds a lots of depth to the sauce. Any type works, but watch out for the saltiness of the darker types.
• a few japanese hot peppers, or sriracha or equivalent.
• a few drops of liquid smoke.

If I don't have ribs to cook but need the sauce, I start it with a demi-glace instead of water, or even with a fond, whatever reduced broth I have left in the freezer.