Mix apple cider vinegar, brown sugar, molasses, honey, Worcestershire sauce, rum, mustard, liquid smoke, red chili pepper and allspice together in a heavy saucepan over medium heat.

Bring to a boil, reduce heat and simmer until sauce is smooth and brown sugar is dissolved, about 5 minutes.

Stir Ketchup into sauce and bring to a boil. Reduce heat and simmer, whisking occasionally, until sauce is dark and thickened, about 30 minutes.