Preheat your oven to 350°F (175°C). Lightly grease a 9x13-inch (23x33 cm) baking pan.
In a large bowl, combine the cake mix, eggs, 2/3 cup eggnog, water, oil, and 1 teaspoon of nutmeg. Beat with an electric mixer on medium speed for 2 minutes until smooth.
Pour the batter into the prepared pan and spread it evenly. Bake for 28 to 30 minutes, or until a wooden skewer inserted into the center comes out clean.
Let the cake cool on a wire rack for 15 minutes. Using the round handle of a wooden spoon, poke holes all over the top of the warm cake, about an inch apart.
In a separate bowl, whisk together the instant pudding mix and 2 cups of cold eggnog until it starts to thicken. Whisk in the spiced rum, if using.
Immediately and slowly pour the pudding mixture over the warm cake, making sure it seeps into the holes.
Cover the cake with plastic wrap and refrigerate for at least 4 hours, or overnight, until the pudding is set.
Once chilled, spread the thawed whipped topping evenly over the cake. Sprinkle with additional ground nutmeg before slicing and serving.