Multi-scenario multi-task recommendation (MSMTR) systems must address recommendation demands across diverse scenarios while simultaneously optimizing multiple objectives, such as click-through rate and conversion rate. Existing MSMTR models typically consist of four information units: scenario-shared, scenario-specific, task-shared, and task-specific networks. These units interact to generate four types of relationship information flows, directed from scenario-shared or scenario-specific networks to task-shared or task-specific networks. However, these models face two main limitations: 1) They often rely on complex architectures, such as mixture-of-experts (MoE) networks, which increase the complexity of information fusion, model size, and training cost. 2) They extract all available information flows without filtering out irrelevant or even harmful content, introducing potential noise. Regarding these challenges, we propose a lightweight Automated Information Flow Selection (AutoIFS) framework for MSMTR. To tackle the first issue, AutoIFS incorporates low-rank adaptation (LoRA) to decouple the four information units, enabling more flexible and efficient information fusion with minimal parameter overhead. To address the second issue, AutoIFS introduces an information flow selection network that automatically filters out invalid scenario-task information flows based on model performance feedback. It employs a simple yet effective pruning function to eliminate useless information flows, thereby enhancing the impact of key relationships and improving model performance. Finally, we evaluate AutoIFS and confirm its effectiveness through extensive experiments on two public benchmark datasets and an online A/B test.