Combine the rum, brown sugar, 2 Tbs. lime juice, and 2 Tbs. butter in a 1-quart saucepan. Bring to a simmer over medium heat and cook until syrupy, about 5 minutes. Stir in 1/8 tsp. salt and remove from the heat.
In a medium bowl, combine the remaining 2 Tbs. lime juice with the oil, allspice, cayenne, 1-1/2 tsp. salt, and 1/2 tsp. black pepper. Add the pork and toss to coat. Thread the pork, bell pepper, and onions onto four 12-inch metal skewers, alternating the meat and vegetables.
Prepare a medium-high (400°F) gas or charcoal grill fire or heat a large grill pan over medium-high heat. Oil the grate or pan. Grill the skewers until seared on all sides, about 4 minutes total. Brush the skewers with the glaze and grill, turning occasionally, until the pork is browned on the outside but still slightly pink in the center, 2 to 4 minutes more.