For the syrup: Combine sugar, water, cherries, and sumac in a medium saucepan over medium-high heat. Bring to a simmer and cook for 10 minutes. Remove from heat. Let stand, covered, for 2 hours. Strain into an airtight container, reserving cherries for garnish. The syrup can be refrigerated for up to 1 week.
For the cocktail: In the bottom of a highball or pilsner glass, add rum, cherry-sumac syrup, and falernum, and fill glass with crushed ice. Throw in a couple of those reserved cherries left over from the syrup too. Using a swizzle stick or bar spoon, rapidly spin back and forth between your hands while also moving it up and down. Add more ice to fill the glass. Garnish with a sprinkle of sumac and several of the reserved cherry quarters from the syrup.