In the bottom of a cocktail shaker, muddle lemon wheel with simple syrup (pound the lemon with the end of a thick wooden spoon or a muddler to extract the juice and the oils from the rind). Add rum, and fill canister halfway with ice. Cover and shake well. Drain into a goblet.
Add 3 ice cubes and red wine to goblet. Stir gently and garnish with a half-slice of lemon.