Given the patchy nature of gas plumes and the slow response of conventional gas sensors, the use of mobile robots for Gas Source Localization (GSL) tasks presents significant challenges. These aspects increase the difficulties in obtaining gas measurements, encompassing both qualitative and quantitative aspects. Most existing model-based GSL algorithms rely on lengthy stops at each sampling point to ensure accurate gas measurements. However, this approach not only prolongs the time required for a single measurement but also hinders sampling during robot motion, thus exacerbating the scarcity of available gas measurements. In this work, our goal is to push the boundaries in terms of continuity in sampling to enhance system efficiency. Firstly, we decouple and comprehensively evaluate the impact of both plume dynamics and gas sensor properties on the GSL performance. Secondly, we demonstrate that adopting a continuous sampling strategy, which has been generally overlooked in prior research, markedly enhances the system efficiency by obviating the prolonged measurement pauses and leveraging all the data gathered during the robot motion. Thirdly, we further expand the capabilities of the continuous sampling by introducing a novel informative path-planning strategy, which takes into account all the information gathered along the robot's movement. The proposed method is evaluated in both simulation and reality under different scenarios emulating indoor environmental conditions.