Pupil reflex to variations in illumination and associated dynamics are of importance in neurology and ophthalmology. This is typically measured using a near Infrared (IR) pupillometer to avoid Purkinje reflections that appear when strong Visible Light (VL) illumination is present. Previously we demonstrated the use of deep learning techniques to accurately detect the pupil pixels (segmentation mask) in case of VL images for performing VL pupillometry. Here, we present a method to obtain the parameters of the elliptical pupil boundary along with the segmentation mask is presented. This eliminates the need for an additional, computationally expensive post-processing step of ellipse fitting and also improves segmentation accuracy. Using the time-varying ellipse parameters of pupil, we can compute the dynamics of the Pupillary Light Reflex (PLR). We also present preliminary evaluations of our deep-learning algorithms on clinical data. This work is a significant push in our goal to develop and validate a VL pupillometer based on a smartphone that can be used in the field.