In a small pot over medium heat, combine the sugar and water. Bring to a boil, stirring to dissolve the sugar completely.
Remove the pot from the heat and stir in the cucumber. Let steep, covered, for at least 4 hours or up to overnight.
Strain the syrup through a fine-mesh sieve or cheesecloth, pushing to extract as much syrup as possible. Store in an airtight container in the refrigerator for up to 1 month.
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In a cocktail shaker filled with ice, combine the gin, watermelon juice, lime juice, and simple syrup. Shake vigorously for 20 seconds.
Strain into a glass filled with ice and top with club soda.