Remote driving relies on continuous Vehicle-to-Satellite (V2S) connectivity in areas lacking terrestrial coverage. While early research focuses on latency and reliability for teleoperation - often evaluated under static or simplified setups these metrics depend on specific channel models and access schemes. This paper instead provides a technology-agnostic analysis of connectivity dynamics that govern Handovers (HOs) in Low Earth Orbit (LEO) satellite networks. Using a high-fidelity simulator with satellite mobility, vehicle movement, and urban obstructions, we evaluate Line-of-Sight (LoS) availability and HO frequency under different strategies. Results show that obstruction topology and HO triggers significantly affect link continuity, with obstacle height having a non-linear impact on HO rates. A key takeaway is also that advance knowledge of satellite and vehicle trajectories can enable more intelligent HO strategies, but only if local obstruction geometry is also considered. These insights establish a baseline for future studies that integrate detailed channel models and assess end-to-end performance.