Using a long serrated knife, cut each cake layer in half horizontally. Place one cake half, browned side down, on a cake platter. Slip strips of waxed paper under the cake to protect the platter during icing. Brush and drizzle about 1 tablespoon of the rum over the cake. Spread with about ¾ cup of the mousse, and evenly scatter about ½ cup of the pineapple on top. Repeat with the remaining two cake layers, 2 tablespoons of rum, 1½ cups of mousse, and 1 cup pineapple. Top with the remaining cake layer, cut side up, and brush with the remaining mousse. Using an icing spatula, frost the top and sides of the cake with the remaining mousse. Do not worry if the mousse doesn’t mask the cake completely, as it will be covered with coconut later. Refrigerate the cake until the mousse is cool and firmer, at least 1 and up to 8 hours.