As a nod to Honeysuckle Farms, we used Mississippi's Cathead Honeysuckle Flavored Vodka.
Process watermelon in a blender or food processor until smooth. Pour through a fine wire-mesh strainer into a large pitcher, using back of a spoon to squeeze out juice; discard solids.
Stir vodka and next 2 ingredients into watermelon juice. Add ice, and top with soft drink; gently stir. Serve immediately.
*Light rum or plain vodka may by substituted.