Research in neuroscience and vision science relies heavily on careful measurements of animal subject's gaze direction. Rodents are the most widely studied animal subjects for such research because of their economic advantage and hardiness. Recently, video based eye trackers that use image processing techniques have become a popular option for gaze tracking because they are easy to use and are completely noninvasive. Although significant progress has been made in improving the accuracy and robustness of eye tracking algorithms, unfortunately, almost all of the techniques have focused on human eyes, which does not account for the unique characteristics of the rodent eye images, e.g., variability in eye parameters, abundance of surrounding hair, and their small size. To overcome these unique challenges, this work presents a flexible, robust, and highly accurate model for pupil and corneal reflection identification in rodent gaze determination that can be incrementally trained to account for variability in eye parameters encountered in the field. To the best of our knowledge, this is the first paper that demonstrates a highly accurate and practical biomedical image segmentation based convolutional neural network architecture for pupil and corneal reflection identification in eye images. This new method, in conjunction with our automated infrared videobased eye recording system, offers the state of the art technology in eye tracking for neuroscience and vision science research for rodents.