Preheat your oven to 350°F and position the rack in the middle. Prepare two 8x4 inch loaf pans by spraying them with non-stick spray or lining them with parchment paper.
In a medium bowl, combine the flour, baking soda, baking powder, salt, cinnamon, nutmeg, and pudding mix. Stir until everything is well mixed.
In a large bowl, whisk together the eggs, vegetable oil, granulated sugar, brown sugar, buttermilk, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring just until everything is incorporated. Gently fold in the shredded zucchini and drained pineapple until evenly distributed.
Divide the batter between the two prepared loaf pans. Place them in the preheated oven and bake for 45-55 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, allow the bread to cool in the pans for a few minutes before transferring them to a wire rack to cool completely.
For the glaze, mix the powdered sugar and reserved pineapple juice in a small bowl until smooth. Drizzle the glaze over the cooled zucchini bread.