In a small saucepan, whisk together all of the ingredients until fully combined.
Place the saucepan over medium heat and bring the mixture to a boil. Cook for 18-20 minutes, stirring occasionally and adjusting the heat as needed. Simmer until the sauce has reduced and thickened enough to coat the back of a spoon. The sauce will continue to thicken as it cools, so be careful to not overcook it. You're looking for a consistency slightly thinner than what you want the finished sauce to be.
Transfer the barbecue sauce to a bowl or container and let it cool to room temperature before using.
Notes
Spiced Rum: Any kind of spiced rum works for this BBQ sauce recipe. Dark rum can be used as a substitute if you don't have spiced.
Ketchup: Can be substituted with tomato paste that has been thinned with a bit of water.
White Vinegar: Apple cider vinegar works well if you don't have white.
Make it Spicy: Add cayenne pepper, chipotle powder, or hot sauce for an extra spicy kick.
Make it Smokier: Add a few drops of liquid smoke for a delicious, punchy smoked flavor.
The barbecue sauce will bubble rapidly on the stove, and this is ok, it is the alcohol cooking off. Adjust the heat as needed so it doesn't boil over, but keep it high enough that it boils rapidly.
Store leftover sauce in an airtight container or jar and keep in the fridge for up to 1 week.