Heat oven to 375° F. In a small bowl, soak the apricots in 3 tablespoons of the wine and set aside. Grease and flour a 9-by-13-inch baking pan. In a large mixing bowl, combine the cake mix, eggs, and oil, along with the amount of water called for by the package directions. Beat until well combined. Evenly spread the batter into the pan. Place in oven and bake until a toothpick inserted into the cake's center comes out clean, 20 to 25 minutes. Let the cake cool in the pan for 15 minutes.
Unmold the cake. Using a 3-inch round cookie cutter, cut 12 rounds from it. Use a serrated knife to split each round in half horizontally. With a pastry or basting brush, brush each of the 24 rounds with some of the remaining wine. To assemble a single serving of trifle, place one round into an individual serving dish. Top with a spoonful of the jam, then 2 tablespoons of the custard. Top with another layer of cake, jam, and custard. Sprinkle with some of the wine-soaked apricots.