Pour water into a saucepan and add tamarind pod pieces, habanero pepper, garlic, salt, and black pepper. Bring to a boil and reduce heat to low; simmer until tamarind pods begin to break down and seeds appear. Stir brown sugar into mixture. Press pods against side of pan with a slotted spoon as they cook to help extract pulp. Discard seeds.
Continue simmering until tamarind mixture thickens to the consistency of tomato soup, about 40 minutes, stirring often. Mix cilantro, lime juice, and vinegar into sauce and simmer just until cilantro is wilted, 1 to 2 more minutes.
Pour sauce through a fine mesh strainer, pressing as much pulp and solids through the mesh as possible. Discard the remaining almost-dry solids (about a palm full) and scrape the outside of the strainer into retained sauce.