To prepare sorbet, combine 4 cups water, 1 cup sugar, and light corn syrup in a medium saucepan; bring to a boil over high heat. Cook 2 minutes or until sugar dissolves, stirring frequently. Scrape seeds from vanilla bean into a medium bowl. Add vanilla bean and fresh lemon juice. Pour hot sugar mixture over vanilla mixture; stir well with a whisk. Cover and chill completely. Remove and discard vanilla bean. Pour mixture into the freezer can of an ice-cream freezer, and freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze for 4 hours or until firm.
To prepare topping, combine dark rum, water, sugar, and ginger in a small saucepan. Bring to a boil; cook 2 minutes. Remove from heat; cool to room temperature. Remove and discard ginger. Pour rum mixture over pineapple; chill 1 hour.