Electrochemical random-access memory (ECRAM) devices are promising cross-point elements for implementing analog cross-point array-based AI computation accelerators due to their remarkable programmability and high-stability driven by ion movement. However, efforts to investigate the fundamental physical parameters governing switching have been limited by the complexity of ECRAM multilayer film structure and the low mobility and high-resistivity of the oxide material. Additionally, tracking the movement of oxygen vacancies within metal oxides has been challenging compared to other active ions. Herein, we fabricate ECRAM devices with multi-terminal Hall-bar structures and conduct AC magnetic parallel dipole line (PDL) Hall measurements. Using two rotating DC magnets and lock-in technique, we extract key transport parameters such as mobility and carrier density of high-resistivity WO3-x channel layer. Through variable-temperature Hall measurements at 50 - 300 K, we experimentally measure, for the first time, the oxygen donor level at approximately 0.1 eV in WO3-x thin film. In addition, we characterize the resistive switching of ECRAM at low temperatures, for the first time, and reveal that the conductance potentiation is caused by increase in both mobility and carrier density. This phenomenon can be attributed to the reversible changes in electronic and atomic structure supported by density functional theory calculation result. Overall, our experimental study on ECRAM switching mechanism contributes to a deep understanding of the operational principles of ECRAM and provides valuable insights for enabling high-performance and energy-efficient AI computation in analog hardware.