In a small bowl, combine the brown sugar, allspice, cinnamon, ginger, onion powder, garlic powder, cayenne pepper, cloves, 1/2 teaspoon of the salt and the black pepper. Rub the spice mixture over the pork and let stand for 15 minutes.
In another small bowl, combine the vinegar, honey, tomato paste and the remaining 1/4 teaspoon salt. Whisk to blend. Set aside.
Prepare a hot fire in a charcoal grill or heat a gas grill or broiler (grill) to medium-high or 400 F. Away from the heat source, lightly coat the grill rack or broiler pan with cooking spray. Position the cooking rack 4 to 6 inches from the heat source.
Place the pork on the grill rack or broiler pan. Grill or broil at medium-high heat, turning several times, until browned on all sides, 3 to 4 minutes total. Remove to a cooler part of the grill or reduce the heat and continue cooking for 14 to 16 minutes. Baste with the vinegar-honey glaze and continue cooking until the pork is slightly pink inside and an instant-read thermometer inserted into the thickest part reads 160 F, 3 to 4 minutes longer. Transfer to a cutting board and let cool for 5 minutes before slicing.
To serve, slice the pork tenderloin crosswise into 16 pieces and arrange on a warmed serving platter, or divide the slices among individual plates.