Preheat the oven to 325 degrees F.
Trim ham of any tough outer skin. Score top in a diamond pattern, making shallow cuts about 1" apart. Bake the ham, uncovered, for 75 minutes.
Meanwhile, make the glaze by placing the juice and rum in a small pot. Simmer and reduce to half its original volume. Remove the pot from the heat and mix in the remaining ingredients.
After 75 minutes, baste the ham with 1/3 of the glaze and bake 10 minutes more. Repeat the basting step twice more. Transfer the ham to a serving platter, tent with foil, rest 15 minutes, and then slice and serve.