I've never tried 'cooking' a fresh rambutan, but one common thing many Cambodians I know (and I would hazard a guess that this is common across Southeast Asia) do with canned rambutan (or lychee, or longan, or jackfruit, or sugar palm nut, or bananas, or beans, or many other kinds of fruit, canned or fresh) is to make a simple little soup dessert.
It consists of using the syrup from the can, or a homemade simple syrup, adding the peeled fruit, cut into pieces if they are too big, and adding a dollop of coconut cream on top.
I prefer this dessert served just slightly warm, with an extra helping of little tapioca balls for a little extra thickness and just the lightest smidgen of salt too for depth.
When we are really being fancy, though, we also add a little bit more coconut milk to the simple syrup (not a lot, though, because of the high fat content), add a dollop of the head of the coconut cream, and sprinkle with toasted sesame seeds and a little shaved coconut too, for texture.
But it's perfectly delicious as well served on ice with the simple syrup, the fruit, and the ice all melding together as a nice cool, watery-sweet refreshing snack (and, I can't help it, just a dollop of coconut cream). Some people also add tapioca in any of its many forms--as tapioca noodles or as the regular pearls. When I'm feeling exotic, I add a little bit of vanilla extract to the mix too.