Position a rack in the center of the oven and preheat to 350°F (175°C). Grease the bottom and sides of a 9-by-13-inch (23-by-33-cm) baking pan with the 1 teaspoon neutral oil.

Place the white cake mix, 1 cup water, 1/2 cup vegetable oil, and 3 egg whites in a large mixing bowl. Beat on low speed for about 30 seconds, until the dry mix is moistened. Increase to medium speed and beat for 2 minutes, scraping the bowl once. The batter should look smooth, pale, and slightly airy.

Spread the batter evenly in the prepared pan. Bake for 28 to 32 minutes, until the top is lightly golden, the center springs back when gently pressed, and a toothpick inserted in the middle comes out clean or with a few moist crumbs. If wet batter remains on the toothpick, bake for another 2 to 3 minutes and check again.

Place the pan on a heat-safe surface and let the cake rest for 10 minutes. Using the handle of a wooden spoon or a thick skewer, poke holes about 1 inch apart across the entire cake. Press nearly to the bottom without tearing large pieces from the surface.

Pour the raspberry gelatin powder into a heatproof measuring cup or bowl. Add 1 cup boiling water and stir for about 2 minutes, until the gelatin is completely dissolved and no grains remain. Stir in the 1/2 cup cold water.

Slowly pour the raspberry mixture over the cake in several passes, concentrating on the holes but covering the full surface. Pause briefly between passes so the liquid can absorb. A small amount may remain visible on top at first, but it should gradually soak in.

Let the cake cool at room temperature for 30 minutes. Cover the pan and refrigerate for at least 3 hours, until the cake is thoroughly cold and the gelatin has set inside the holes.

Beat the softened cream cheese, powdered sugar, and vanilla extract on medium speed for 1 to 2 minutes, until smooth and free of lumps. Fold in the thawed whipped topping until evenly blended, then fold in 1 cup (85 g) of the shredded coconut. The topping should be fluffy but sturdy enough to hold soft swirls.

Spread the topping evenly over the chilled cake with an offset spatula. Sprinkle the remaining 1/4 cup (20 g) shredded coconut over the surface. Add the fresh raspberries, if using.

Keep the cake refrigerated until serving. Cut it into 15 slices using a clean, sharp knife, wiping the blade between cuts for neater layers.