Combine flour, baking powder, and ½ teaspoon salt, stirring well. Place sugar, butter, and cream cheese in a large bowl; beat with a mixer at high speed until light and fluffy.
Add eggs, 1 at a time. Beat in oil, rind, and vanilla. Add flour mixture and milk alternately to batter, beginning and ending with flour.
Spoon batter into a 10-inch tube pan with greased with butter. Bake at 160°C for 1 hour and 10 minutes or until a wooden pick inserted in center comes out with moist crumbs clinging.
Cool in pan on a wire rack 10 minutes. Invert cake. Cool on rack.
Place grapefruit juice in a saucepan over medium-high heat; bring to a boil. Cook until reduced to 3 tablespoons (about 4 minutes). Cool slightly. Stir in powdered sugar and remaining ⅛ teaspoon salt. Drizzle over cake.