Rinse the goat meat in cool water with the lime or lemon juice. Drain well and set aside.
In a pilón or mortar and pestle, mash the garlic, ají gustoso peppers, salt, and oregano into a coarse paste.
Place the meat in a large bowl. Add the garlic paste, adobo, black pepper, bitter orange juice, and rum. Mix well to coat. Cover and marinate in the refrigerator for at least 4 hours, preferably overnight.
Heat the oil in a large pot or caldero over medium-high heat. Add the marinated meat, reserving the marinade. Cook, stirring occasionally, until the meat releases its liquid and begins to brown, about 5 minutes.
Continue cooking, stirring occasionally, for about 25 to 30 minutes, or until most of the liquid has evaporated and the meat starts to sear.
Add the reserved marinade and 3 cups of water. Stir to combine.
Reduce the heat to medium and simmer, stirring occasionally, for about 45 minutes. Add additional water, 1 cup at a time, as needed to keep the meat cooking in liquid. Cook until the sauce reduces and the meat is very tender.
Stir in the tomato sauce, sliced pepper, onion, tomato, culantro, and olives. Cook for 10 to 15 minutes, or until the vegetables are softened and the sauce thickens.
Serve warm.