Step 1: Place the pineapple juice in a spray bottle or in a bowl and set it aside.
Step 2: Place the brown sugar, paprika, salt, cinnamon, fennel seed, granulated onion and garlic, caraway seed, ginger, pepper, and cloves in a small bowl and mix with your fingers, breaking up any lumps in the brown sugar.
Step 3: Prepare the ribs: Place a rack of ribs meat side down on a baking sheet. Remove the thin, papery membrane from the back of the rack by inserting a slender implement, such as a butter knife or the tip of a meat thermometer, under it. The best place to start is on one of the middle bones. Using a dishcloth, paper towel, or pliers to gain a secure grip, peel off the membrane. Repeat with the remaining rack.
Step 4: Sprinkle the rub over both sides of the ribs, rubbing it onto the meat. Cover the ribs with plastic wrap and refrigerate them while you set up the grill.
Step 5: Thread the ribs onto the rotisserie spit: Place a rack of ribs bone side up on a work surface. Using a sharp, slender knife, make starter holes in the center of the meat between every 4th or 5th rib. Twist the knife blade to widen the holes; this will make it easier to insert the spit. Repeat with the remaining rack of ribs. Use an over and under weaving motion to thread the spit through the holes in the racks of ribs.
Step 6: Set up the grill for spit roasting following the manufacturer’s instructions and preheat to high. Place a large drip pan in the center of the grill directly under the spit.
Step 7: When ready to cook, attach the spit to the rotisserie mechanism, turn on the motor, and cover the grill. After 20 minutes, spray the ribs with the pineapple juice. Cook the ribs until they are golden brown and cooked through, 30 to 45 minutes, spraying with pineapple juice every 10 minutes. When the ribs are done, the meat will have shrunk back from the ends of the bones by about 1/4 inch.
Step 8: Just before you are ready to remove the ribs from the spit, brush them on both sides with the Ginger-Pineapple-Rum Barbecue Sauce. Let them continue to turn on the spit until the sauce is sizzling, about 2 to 3 minutes.
Step 9: Transfer the spit with the ribs to a cutting board. Carefully remove the skewer, then let the ribs rest for a few minutes. Serve the racks, whole or cut into individual ribs, with the remaining Ginger-Pineapple-Rum Barbecue Sauce.