Trim fat from meat. If necessary, cut meat to fit into a 3-1/2- or 4-quart slow cooker. Sprinkle jerk seasoning evenly over meat; rub into meat with your fingers. Place meat in slow cooker. Sprinkle with thyme. Pour the water over meat in cooker.
Cover and cook on low-heat setting for 8 to 10 hours or on high-heat setting for 4 to 5 hours.
Transfer meat to a cutting board; cool meat slightly. Using two forks, shred meat, discarding fat. Place meat in a medium bowl. Stir lime juice into meat.
If desired, line tortillas with lettuce leaves. Divide meat mixture among tortillas, placing meat in center of each tortilla. Top with sweet pepper, mango, and Lime Mayo. Fold bottom half of each tortilla over filling; fold in sides. Roll up.
In a small bowl stir together mayonnaise, onion, lime peel, lime juice, and garlic. Store in a tightly covered container in the refrigerator for up to 1 week.