Combine raisins and rum in a small bowl and let sit 30 minutes.
Using an electric mixer, beat eggs and granulated sugar at high-speed until thick and pale, about 2 to 4 minutes. Add oil and vanilla and beat just until blended. Add mashed sweet potatoes and beat just until blended, scraping down sides of bowl as needed.
Preheat oven to 350 degrees.
Place flour, cinnamon, baking powder, baking soda, salt, nutmeg, and allspice into a medium bowl and whisk together. With mixer on low speed, add flour mixture to egg mixture, alternating with buttermilk, beginning and ending with flour mixture.
Drain raisins and reserve rum. Fold raisins into batter.
Spoon batter into lightly greased mini-Bundt pans. (I used the ones that make 6 cakes per pan. You will have enough batter for at least 3 pans worth. If you only have one pan, you can cook the cakes in 3 batches. Let the pan cool before batches.) Fill just over ¾ of the way full.
Bake for 13 to 15 minutes, or until firm to the touch on top. Cool in pans set on wired racks for 5 minutes. Spray wire racks lightly with cooking spray before inverting cakes onto racks to finish cooling.
While cakes bake, bring dark brown sugar, butter, and whipping cream to a boil in a small heavy-bottomed saucepan. Boil for 3 minutes, stirring constantly. Once mixture becomes syrup-like consistency, remove from heat and stir in reserved rum.
Use a wooden pick to poke holes in tops of cakes. Dip tops of cakes into glaze, letting them soak up the glaze for a few seconds. Turn right side up and sprinkle with pecans.
Serve warm or at room temperature.