Spatio-Temporal Graph Neural Networks (STGNNs) are neural network models that integrate spatial information into time series processing, and have been successfully applied in various applications. Although these models have demonstrated strong prediction capabilities, most existing STGNN architectures require a significant memory size and long training times. Some lightweight versions of STGNNs have been proposed, but they still rely on expert-driven manual designs to improve performance, which require implicit domain-specific knowledge that varies across datasets. This design approach limits their adaptability to different application scenarios. To address this limitation, Neural Architecture Search (NAS) has been applied to automate the STGNN design process. However, existing NAS-based approaches prioritize prediction accuracy rather than resource efficiency. As a result, current approaches fail to provide compact model architectures or efficient training and limit their scalability. In this work, we introduce SearchLight, a novel NAS-based STGNN framework to automatically discover lightweight STGNN models while maintaining prediction performance. We set two cells for spatial and temporal operations into two distinct sets to capture spatial and temporal data features better for each cell type of the NAS method. We specialize in cell types for spatial and temporal information so that the model can better capture and combine the intrinsic features of spatial and temporal data. We employ a multi-objective search strategy that optimizes both model compactness and prediction accuracy to enable our method to discover lightweight and accurate STGNN models. Experimental results across several real-world datasets show that SearchLight reduces the model size by an average of <inline-formula> <tex-math notation="LaTeX">$\times 103.0$ </tex-math></inline-formula> and training time by an average of <inline-formula> <tex-math notation="LaTeX">$\times 74.0$ </tex-math></inline-formula>, while sacrificing a small amount of prediction performance, an average of 1.6%p, compared to manually designed and existing NAS-based STGNN models.