Fill a mug with hot water and let it stand for 1 to 2 minutes to warm it.
To make Turmeric-Ginger Honey Syrup: Whisk together the turmeric and ginger juices and honey until well combined. Store in an air-tight container in the refrigerator for up to 1 week.
Empty the mug and fill it with the lemon juice, syrup, vinegar, pepper, and 5 ounces hot water. Stir to combine. Garnish with the clove-studded lemon wheel.
Batch for 6: Fill a 6-to-8-cup thermos with 3 3⁄4 cups hot water. Add 1⁄2 cup plus 1 Tbsp. freshly squeezed lemon juice, 1⁄2 cup plus 1 Tbsp. syrup, 1⁄4 cup plus 2 Tbsp. apple cider vinegar, and 1⁄4 tsp. cayenne pepper. Stir to combine, then divide among 6 pre-warmed mugs. Garnish each with a clove-studded lemon wheel.