In a small, heavy bottomed saucepan over medium-high heat, combine 1 cup granulated sugar and 1 cup water. Whisk until the sugar dissolves, and bring the mixture to a boil. Remove from heat and set aside on a wire rack to cool to room temperature. Transfer to a glass jar with a lid and chill in the refrigerator for up to 1 week.
For the Red Wine Gin Sour
Combine the gin, elderflower liqueur, simple syrup, freshly squeezed lemon juice, and egg white in a metal cocktail shaker. Shake with the metal coil from a Hawthorne strainer for 15 to 20 seconds.
Add ice to the shaker and shake vigorously for another 15 to 20 seconds. Strain into an empty shaker with no ice and shake vigorously for 15 to 20 seconds more.
Transfer the mixture to a tall glass with ice, and finish the drink off by pouring red wine over the back of a bar spoon over the center of the glass. Given its weight, the wine will automatically sink below the foam to create that pretty ombre layered effect. Serve immediately.