We report how analysis of the spatial and temporal optical responses of liquid crystal (LC) films to targeted gases, when performed using a machine learning methodology, can advance the sensing of gas mixtures and provide important insights into the physical processes that underlie the sensor response. We develop the methodology using O3 and Cl2 mixtures (representative of an important class of analytes) and LCs supported on metal perchlorate-decorated surfaces as a model system. Although O3 and Cl2 both diffuse through LC films and undergo redox reactions with the supporting metal perchlorate surfaces to generate similar initial and final optical states of the LCs, we show that a three-dimensional convolutional neural network can extract feature information that is encoded in the spatiotemporal color patterns of the LCs to detect the presence of both O3 and Cl2 species in mixtures and to quantify their concentrations. Our analysis reveals that O3 detection is driven by the transition time over which the brightness of the LC changes, while Cl2 detection is driven by color fluctuations that develop late in the optical response of the LC. We also show that we can detect the presence of Cl2 even when the concentration of O3 is orders of magnitude greater than the Cl2 concentration. The proposed methodology is generalizable to a wide range of analytes, reactive surfaces, and LCs and has the potential to advance the design of portable LC monitoring devices (e.g., wearable devices) for analyzing gas mixtures using spatiotemporal color fluctuations.