When working under the eyes, have your model look upwards - only with the eyes, without moving the head. If you work above the eyes (eyelid), have your model close his/her eyes in a relaxed manner. Children are inclined to shut their eyes tight. Then you can say: keep your eyes closed as if you are sleeping.
Draw the stripes with a flat brush. Do try to keep the lines running parallel, otherwise it starts to look messy. You can simply let the lines run into the hair.