I took the easy way and used some high-quality grapefruit juice from the grocery store. However, if you would prefer to do fresh, plan on juicing about one or two large grapefruits!
In a small saucepan, combine the sugar, water, and a few leaves of fresh sage. Bring to a simmer, pressing on the sage with the back of a spoon to release the oils. After a couple of minutes, remove from heat and let cool completely.
To make the greyhounds, combine the grapefruit juice, vodka, and sage simple syrup in a cocktail shaker. Fill with ice, and shake until the outside starts to get frosty, about 20-30 seconds. Strain into two martini glasses. Twist a sage leaf over each cocktail to release the oils. Garnish the cocktail with fresh sage. Serve!