Deepfakes are a major security risk for biometric authentication. This technology creates realistic fake videos that can impersonate real people, fooling systems that rely on facial features and voice patterns for identification. Existing multimodal deepfake detectors rely on conventional fusion methods, such as majority rule and ensemble voting, which often struggle to adapt to changing data characteristics and complex patterns. In this paper, we introduce the Straight-through Gumbel-Softmax (STGS) framework, offering a comprehensive approach to search multimodal fusion model architectures. Using a two-level search approach, the framework optimizes the network architecture, parameters, and performance. Initially, crucial features were efficiently identified from backbone networks, whereas within the cell structure, a weighted fusion operation integrated information from various sources. An architecture that maximizes the classification performance is derived by varying parameters such as temperature and sampling time. The experimental results on the FakeAVCeleb and SWAN-DF datasets demonstrated an impressive AUC value 94.4\% achieved with minimal model parameters.