Place the water, guava paste, vinegar, rum, tomato paste, lemon juice, onion, ginger, soy sauce, tomato sauce, Worcestershire sauce, garlic and chilli pepper into a saucepan. Bring to a simmer over medium-high heat, whisking until evenly blended. Season to taste with salt and pepper.
Reduce heat to medium-low and simmer until the sauce has slightly thickened and is richly flavoured, 10 to 15 minutes. The sauce should be pourable. If it has become too thick thin it with some water. Serve hot or cold.