With the tip of a sharp knife, score the fat coating in ¼-inch deep rows about 1-inch apart in two directions to form a diamond pattern. Place the ham, with the fat cap up, in a large roasting pan. Roast in the lower third of the oven for 1 hour 30 minutes.
Meanwhile, combine the ginger ale, ginger, rum and brown sugar in a medium saucepan. Bring to a boil over high heat and cook until mixture is slightly syrupy and reduced to 1 cup, about 45-47 minutes. Stir in the mustard.
After the ham has roasted for 1 hour 30 minutes, baste it with some of the ginger glaze. Continue roasting and basting the ham about every 20 minutes with the glaze until glossy and an instant read thermometer inserted into the thickest portion of the ham registers 140°F, about 2-2 1/2 hours longer. Remove from the oven and let rest 20-30 minutes before slicing.