Place strawberry Balsamic Vinegar in a small pot and reduce by ½ or more until thick and syrup
While the Balsamic vinegar is reducing, place butter and rum into a small dish and heat in a microwave until butter is just melted.
Place peach halves, cut side up, on a large piece of aluminum foil. (Note, dividing the peaches into two batches will make handling them easier. Use 4 halves per piece of foil)
Combine brown sugar and cinnamon and distribute evenly into center of each peach half.
Brush the peaches with the rum-butter mixture, and fold the foil over the peaches and seal.
Place peach bundles on grill over medium heat.
Cook 15 minutes or until peaches are thoroughly heated and softened.