In a medium nonreactive saucepan, stir together the vinegar, spiced rum, sugar, onions, ginger and mustard seeds until the sugar dissolves. Bring to a boil over high heat. Adjust heat so the mixture boils gently and cook for 15 minutes to reduce the mixture slightly. Remove pan from the heat.
Peel and core the pears. Cut them into 1/4 inch chunks.
Immediately stir the pear chunks into the vinegar mixture to prevent discolouring.
Return the saucepan to the heat. Bring mixture to a simmer over medium high heat. Add the tomatoes. Reduce the heat and simmer, stirring occasionally for 50 minutes longer, or until the pears have cooked down and are softened but still retain some shape. (The chutney will be just slightly fluid but will thicken when chilled.) Let cool briefly.
Pour the chutney into glass storage jars. Cover and refrigerate for at least 3 hours or until thoroughly chilled and slightly thickened.