Soak wooden skewers in water at least 1 hour before broiling or grilling.
For chutney, stir together brown sugar, vinegar, garlic, ginger and cinnamon in a medium saucepan. Add apples, apricots, onion, and 1/2 teaspoon thyme. Cover and bring to boiling over medium heat. Reduce heat and boil gently for 10 minutes. Uncover and boil gently about 5 minutes more or until desired consistency. (A small amount of liquid should remain.) Remove from heat. Cool slightly. To serve, transfer to a serving bowl. Or to store, transfer to a container with a lid; cover and chill up to 2 days; let stand at room temperature for 30 minutes before serving.
Meanwhile, stir together apple juice, mustard, and 1/2 teaspoon thyme in a small bowl; set aside. Cut pork across the grain into thin slices, then cut slices into strips about 1 inch wide. Loosely thread each pork strip accordion-style onto two side-by-side wooden skewers. Lightly brush mustard mixture on all sides of pork. Place skewers on the unheated rack of a broiler pan. Broil 5 to 6 inches from the heat for 7 to 8 minutes or until cooked through, turning once. (Or, grill skewers on the rack of an uncovered grill directly over medium-hot coals for 7 to 8 minutes or until cooked through, turning once.)
To serve, transfer skewers to a serving platter; serve with chutney. Makes 20 to 24 appetizer servings.