This study addresses the motion and inertia parameter estimation problem of a torque-free, tumbling, non-cooperative space object (target) under long-term occlusions. To solve this problem, we employ a data-driven Gaussian process (GP) to simulate sensor measurements. In particular, we implement the multi-output GP to predict the projection measurements of a stereo-camera system onboard a chaser spacecraft. A product kernel, consisting of two periodic kernels, is used in the GP models to capture the periodic trends from non-periodic projection data. The initial guesses for the periodicity hyper-parameters of the GP models are intelligently derived from fast Fourier transform (FFT) analysis of the projection data. Additionally, we propose an unscented Kalman filter-Gaussian process (UKF-GP) fusion algorithm for target motion and inertia parameter estimation. The predicted projections from the GP models and their derivatives are used as the pseudo-measurements for UKF-GP during long-term occlusion. Results from Monte Carlo (MC) simulations demonstrate that, for varying tumbling frequencies, the UKF-GP can accurately estimate the target's motion variables over hundreds of seconds, a capability the conventional UKF algorithm lacks.