Step 1: Remove and discard the fat just inside the body cavities of the duck. Remove the package of giblets and set aside for another use. Rinse the duck inside and out under cold running water, then drain and blot dry, inside and out, with paper towels.
Step 2: Place the duck on its breast so the back side is up. Using the tip of a sharp, slender knife, make 1 slit in the fatty part of the duck under each wing and 1 slit in the underside of each thigh. Insert a sliver of garlic and a slice of ginger into each slit, then place the remaining garlic and ginger in the body cavity. Prick the duck skin all over with a fork, being careful not to pierce the meat; then season the duck, inside and out, very generously with salt and pepper.
Step 3: Tightly truss the bird with butcher’s string.
Step 4: Make the basting mixture/sauce: Combine the hoisin sauce, rice wine, honey, garlic, and ginger in a bowl and whisk to mix. Add rice wine as needed to thin the sauce to basting consistency. Set aside about 1/2 cup to use for serving.
Step 5: Set up the grill for rotisserie cooking. If using charcoal, light 50 to 60 coals and let them burn down until glowing red and covered with a thin coat of ash. Rake one row of coals just in front of the place the duck will be turning and one row just behind it. Place a drip pan between the rows of coals directly under the grate beneath the place where the duck will be roasting. If using a gas grill, turn the front and rear burners on high and leave the middle burner off. Put the drip pan in the center.
Step 6: Place the duck on the spit according to the manufacturers directions, then insert the spit into the motor. Turn the rotisserie on. Cover the grill and cook for 1-1/4 to 1-1/2 hours, or until the skin is mahogany brown and crackling crisp and the meat is well done and tender, another 30 to 60 minutes. Start basting with the basting mixture/sauce the last 30 minutes. An instant-read thermometer inserted in the thigh, not touching the bone, should register 170°F. If using a charcoal grill, add 10 to 12 fresh prelighted coals per side after each hour of cooking.
Step 7: Carefully remove the duck from the spit. Transfer to a platter and let rest for 5 minutes before carving. To eat, put duck meat in flour tortillas and top with cucumbers and hoisin sauce.