1. Preheat oven to 375°.
2. Coat a 10-inch tube pan with cooking spray; sprinkle pecans in bottom of pan.
3. Combine 1 cup water and 1/2 cup sugar in a small saucepan. Bring to a simmer over medium heat; cook 10 minutes or until mixture is reduced to 3/4 cup. Remove from heat; stir in rum.
4. Combine milk and butter in a small saucepan. Cook over medium heat 3 minutes or until butter melts. Remove from heat; cool 5 minutes.
5. Weigh or lightly spoon flours into dry measuring cups; level with a knife. Combine flours, 1/2 cup sugar, baking powder, and xanthan gum in a medium bowl; stir with a whisk. Add vanilla, eggs, and milk mixture; beat with a mixer at medium speed until well blended. Spoon batter over pecans in pan; sharply tap pan once on counter to remove air bubbles.
6. Bake at 375° for 30 minutes or until a wooden pick inserted in center comes out clean. Cool 10 minutes in pan on a wire rack. Remove from pan; place on a serving plate.
7. Brush rum syrup over cake; let stand 10 minutes. Repeat twice, reserving 1/3 cup rum syrup for serving. Spoon whipped topping and reserved rum syrup over slices of cake.