Combine the dried fruits, both zests, and the candied ginger in a plastic storage container. Add the rum, cover, and macerate overnight at room temperature.
The next day, load up a coffee/spice grinder or spice mill with the cloves, allspice, and cinnamon and grind to a fine powder.
Add the spices, along with the macerated fruit and its liquid to a large saucepan. Add the sugar, butter, apple juice, and ginger. Bring to a boil, stirring often, then reduce the heat and simmer for 10 minutes. Remove from the heat and cool for at least 15 minutes. (At this point, you can either complete the batter or cover and refrigerate for up to 2 days, which is what I usually do.)
Place oven racks in the center and bottom of the oven. Place a roasting pan on the bottom rack and fill halfway with warm water. Crank the oven to 325ºF.
Put the flour, salt, baking soda, and baking powder in a sifter and sift onto the cooled fruit mixture in the saucepan, bringing the batter together as quickly as possible with a large wooden spoon. One at a time, stir in the eggs. Finally, fold in the pecans.
Spoon the resulting goo into a 10-inch nonstick loaf pan and bake until the interior temperature hits 200°F, about 1 hour.
Remove to a wire rack or trivet. Spritz the top with brandy and cool completely. Wrap the cake in a few layers of cheesecloth, spritz with more brandy, and stash in a tin or any other airtight, food-safe containment vessel.
Every 2 to 3 days, feel the cake and, if dry, spritz with more brandy. The cake's flavor and texture will enhance considerably over the next 2 weeks. If you decide to give the cake as a gift, be sure to tell the recipient that they are very lucky indeed.