For the cocktail: In a blender, puree the lychees with 1/4 cup of the reserved syrup until smooth. Freeze for about 1 hour to chill.
For the blood drip glasses: On a plate, mix the corn syrup and food coloring until fully combined. Dip 4 coupe glasses a couple times in the corn syrup mixture, swirling to cover the rims. Turn the glasses right-side up, let the syrup drip down the sides and then set on wax paper to dry, about 5 minutes.
For the lychee eyeballs: Insert a blueberry into the hole of the 4 reserved lychees.
Finish the cocktail: Add 3 tablespoons of the chilled lychee puree to each of the blood drip glasses. Fill to the top with ginger beer and a splash of lychee juice. Stir gently.