Sparkling Grapefruit Cocktail

Coarse sugar or salt 1/2 cup freshly squeezed grapefruit juice, from 1 grapefruit 1/4 cup freshly squeezed lime juice, from 1-2 limes 1/2 cup vodka or clear tequila 2 tbsp. simple syrup* 3/4 cups club soda, divided