Soak the corn husks in a bowl of hot water, using a plate to keep them submerged, until pliable, 1 hour.
Meanwhile, make the dough: Mix the masa harina and 1 teaspoon salt in the bowl of a stand mixer. Add 10 tablespoons butter and 3/4 cup warm water and mix with the paddle attachment until combined. Add the granulated sugar, 1/4 cup brown sugar, the almond and vanilla extracts and ground cinnamon; mix until combined, about 1 more minute. Cover and refrigerate.
Make the filling: Simmer 1/2 cup water and the cinnamon stick in a saucepan until slightly reduced, about 10 minutes. Melt the remaining 4 tablespoons butter in a skillet over medium-high heat. Add the remaining 2 tablespoons brown sugar and cook, stirring to dissolve, about 1 minute. Add the pineapple, honey and cinnamon water, including the cinnamon stick; cook, stirring, until the mixture is almost dry, about 5 minutes.
Remove the pan from the heat. Add the rum, then return to medium heat. Tilt the pan so the rum ignites (or hold a lit match near the sauce to ignite it). Cook until the pineapple is slightly caramelized, about 3 minutes. Stir in the pecans; set aside to cool.
Drain the husks and pat dry. Tear each husk lengthwise into a 3 1/2-inch-wide piece. Tear some of the excess husks into 18 thin strips for ties; reserve the husk scraps. Lay the 3 1/2-inch-wide husks on a clean surface. Starting 1/2 inch from the wide end, spread 1 tablespoon of the dough down a husk, leaving a 1/2-inch border on the sides. Spoon 1 tablespoon of the pineapple filling down the center of the dough. Roll lengthwise into a tight cylinder. Fold up the narrow end; tie with a strip of corn husk to secure. Repeat with the remaining husks, dough and filling.
Set a steamer basket in a large pot filled with 1 to 2 inches of water. Set a small bowl upside down in the basket, then arrange the tamales standing up in the steamer, folded-side down, leaning against the bowl. Cover with husk scraps, then lay a damp kitchen towel on top. Bring the water to a boil over medium-high heat, cover and steam until the tamales pull away from the husks, about 40 minutes. Remove from the steamer and let cool slightly before unwrapping.