Photosensor oculography (PS-OG) eye movement sensors offer desirable performance characteristics for integration within wireless head mounted devices (HMDs), including low power consumption and high sampling rates. To address the known performance degradation of these sensors due to HMD shifts, various machine learning techniques have been proposed for mapping sensor outputs to gaze location. This paper advances the understanding of a recently introduced convolutional neural network designed to provide shift invariant gaze mapping within a specified range of sensor translations. Performance is assessed for shift training examples which better reflect the distribution of values that would be generated through manual repositioning of the HMD during a dedicated collection of training data. The network is shown to exhibit comparable accuracy for this realistic shift distribution versus a previously considered rectangular grid, thereby enhancing the feasibility of in-field set-up. In addition, this work further demonstrates the practical viability of the proposed initialization process by demonstrating robust mapping performance versus training data scale. The ability to maintain reasonable accuracy for shifts extending beyond those introduced during training is also demonstrated.