Grease and lightly flour eight 1-cup fluted tube pans or six 4-1/2x2-1/2x1-1/2-inch individual loaf pans and set pans aside.
In a medium bowl combine flour, baking powder, and baking soda; set aside.
In a large bowl beat butter with an electric mixer on medium to high speed for 30 seconds, add brown sugar; beat until combined.
Add eggs, one at a time, beating on medium speed until combined (The batter may appear curdled).
Combine 1/4 cup rum or pineapple juice, 1/4 cup pineapple juice, the corn syrup, ginger, and vanilla.
Add flour mixture and rum mixture alternately to butter mixture, beating on low speed after each addition just until combined.
Fold in fruit bits and nuts.
Spread batter in prepared pan.
Bake in a 325 degree oven for 20 to 25 minutes for fluted tube pans or 30 to 35 minutes for loaf pans or until a toothpick inserted into centers comes out clean.
Cool cakes in pans on wire racks for 10 minutes. Remove from pans; cool at least 1 hour on racks.
Poke holes in cakes using a wooden toothpick or bamboo skewer.
Soak eight or six 8-inch-square pieces of double thickness 100-percent cotton cheesecloth with the 1/3 cup rum or pineapple juice and wrap each cake in rum- or juice-soaked cheesecloth.
Wrap each cake tightly in foil or seal in a plastic bag.
Chill in refrigerator for 24 hours.
Remove foil or remove cakes from bags; drizzle with 1/4 cup rum or pineapple juice. Rewrap with foil or return to plastic bags and refrigerate at least 24 hours.
Remove cheesecloth before serving.
If desired, sprinkle with sifted powdered sugar. Makes 6 or 8 cakes (24 servings).
Make-Ahead Tip: Prepare Tropical Fruit Cake as directed through until the 24 hr chill, except refrigerate up to 5 days. (Or prepare Tropical Fruit Cakes as directed through up to 24 hr chill, except do not sprinkle with powdered sugar. Place in self-sealing freezer bags. Seal, label, and freeze up to 3 months.)
To serve, thaw frozen cakes in freezer bags in the refrigerator overnight. Serve as directed.