An advanced Watt class Hall Micro Thruster (HMT) is offered for Space Gravitational Wave Detection (SGWD), and an investigation has been conducted on its start-up, shutdown, rise, and fall response times. The research involved creating a circuit for thruster discharge and signal acquisition, using a Faraday probe to measure the plasma plume signal generated by the thruster, and characterizing the thrust directly. Ultimately the response time of the thruster is extracted from the discharge current and Faraday current signals. The experimental results demonstrate that the HMT has a response time ranging from 1.08 ms to 16.76 ms at mass flow rates of 0.02 mg/s and 0.04 mg/s, meeting the SGWD requirements for micro thruster response time. This research provides a physical foundation and explanation for the variation of HMT response time with discharge voltage versus mass flow rate with several key parameters that affect HMT plasma discharge, such as neutral gas number density (nn) and ionization mean free path (λi). Furthermore, we have examined several anomalies in the signal. Overall, this research provides a brand-new method for measuring the thrust response time of electric thrusters.