Step 1Set a fine-mesh sieve over a 2-cup glass liquid measuring cup and pour the lychees into it. Shake the sieve gently to drain all the liquid. You should have about 1 cup liquid. If not, add enough water to make 1 cup and stir well.
Step 2Pour ¼ cup lychee syrup into a shallow bowl. Sprinkle the gelatin evenly over the liquid. It should moisten evenly then soften as it sits for 5 minutes. Microwave the remaining lychee syrup until bubbling, 1 to 2 minutes. Scrape the softened gelatin into the bubbling syrup and stir until it dissolves. Stir in the vodka until well mixed.
Step 3Arrange the lychees in mini muffin cups so that the open sides are upright. Pour the syrup into the lychee cavities and around the lychees to fill each muffin cup nearly to the rim. Place a blueberry in each lychee cavity, stem side down, to form the pupils of the eyeballs. Pour the remaining lychee liquid into muffin cups. Refrigerate until very firm, at least 4 hours and up to overnight.
Step 4When ready to serve, slide an offset spatula or thin butter knife around the edge of a muffin cup and pop out the Jell-O shot. Arrange on a serving platter. Pop out the shots without lychees and break them into bits with your fingers to scatter around the shots.
Step 5If the jam is seeded or chunky, press through a fine-mesh sieve. Put the strained jam into a piping bag or resealable plastic zip-top bag. Snip a very small hole in one corner. Pipe the jam around the berries on the lychees to make the eyes look bloodshot. Pipe any remaining jam around the platter to resemble drips of blood.