In recent years, there has been a growing interest in investigating the potential of emerging memristor (MR) devices for gas sensing applications, particularly at room temperature. This article reports on a planar Au/reduced graphene oxide (rGO)/Au memristive hydrogen sensor, fabricated on a cost-effective cyclic olefin copolymer (COC) substrate, and utilizing the rGO green carbon material as its active sensing element. The sensor's performance is evaluated using two different testing modes: conventional chemiresistive testing under a constant voltage bias (CVB) and voltage pulse (VP) modes. The CVB mode demonstrates high repeatability, selectivity, response time, and recovery time, indicating the sensor's reliable gas sensing capabilities. In addition, the VP mode significantly enhances the sensor's relative percentage response, indicating its potential for improved gas sensing performance. To optimize the sensor's response, the impact of hydrogen exposure on the MR resistive switching is studied, revealing that the effect is contingent on the VP amplitude. Specifically, gas-enhanced resistive switching is achieved at lower voltage levels, whereas at higher voltage levels, gas exposure slows down the rate of resistive switching. Consequently, voltage-pulse testing is conducted at two voltage magnitudes, low (2.5 V) and high (4.5 V), and the sensor's response is enhanced from 0.5% under CVB mode to 786% under VP mode.