1. Syrup: Bring the equal amounts of the sugar and water to a boil in a small saucepan, stirring to dissolve sugar. Remove from heat, add thyme sprigs, and cover. Let stand 10 minutes, then strain into a small jar. Let cool entirely
2. Mix thyme syrup, apple cider, rum, lime juice, and bitters in a large pitcher. Divide among glasses filled with ice and top with a splash of club soda. Drizzle with Juna Balanceor Balance X. Garnish with thyme sprigs and lime slices.