Combine the ingredients for the rice and start cooking per the instructions on the rice cooker or package.
While the rice is cooking, preheat your grill for direct cooking. Slice the sausage into thirds, then cut the pieces into halves horizontally. Brush them with enough glaze to give them a coat. Grill covered for 3-5 minutes, flip, and reglaze.
Grill for 3-5 more minutes, flip, and reglaze. Remove the sausage, slice it, and add it to the rice.