The study of human gaze behavior in natural contexts requires algorithms for gaze estimation that are robust to a wide range of imaging conditions. However, algorithms often fail to identify features such as the iris and pupil centroid in the presence of reflective artifacts and occlusions. Previous work has shown that convolutional networks excel at extracting gaze features despite the presence of such artifacts. However, these networks often perform poorly on data unseen during training. This work follows the intuition that jointly training a convolutional network with multiple datasets learns a generalized representation of eye parts. We compare the performance of a single model trained with multiple datasets against a pool of models trained on individual datasets. Results indicate that models tested on datasets in which eye images exhibit higher appearance variability benefit from multiset training. In contrast, dataset-specific models generalize better onto eye images with lower appearance variability.