Add the sugar and water to a small sauce pan and place it over medium-high heat. Heat just until the sugar has dissolved, then pour this into a small bowl to cool. (This is called simple syrup.)
Peel and pit the rambutans. A ripe rambutan should be easy to peel with your fingers. (You might need to make a small cut at the top to get you started.) Be very gentle as you carefully remove the thin skin from the fruit. It will likely come off in just a few pieces.
Now use your fingers to dig into the flesh of the rambutan to remove the pit. It should very easily slide right out. Now use your fingers to dig into the lychee a bit to remove the pit.
You’ll notice a very thin, white layer from the white pit, that will remain on the the inside of the fruit. Don’t try to remove this — it’s very soft and doesn’t detract from the flavor of the fruit. (If you try to remove it, you might loose a lot of juice in the process.)
Place the rambutan in a cocktail shaker or a wooden spatula.)
Add the vodka, lime juice, vanilla, ice, and cooled simple syrup. Cover and shake fairly vigorously for about 30 seconds.
Strain into two martini glasses and add a few of the pieces of the rambutan flesh that you strained out as well.
Garnish each glass with a small lime wedge and part of the rambutan skin. (Use a paring knife to make a small slit in each, to attach it to the rim of the glass.)