Event cameras provide exceptionally high temporal resolution in dynamic vision systems due to their unique event-driven mechanism. However, the sparse and asynchronous nature of event data makes frame-based visual processing methods inappropriate. This study proposes a novel framework, Event-based Graph Spatiotemporal Sensitive Transformer (EGSST), for the exploitation of spatial and temporal properties of event data. Firstly, a well-designed graph structure is employed to model event data, which not only preserves the original temporal data but also captures spatial details. Furthermore, inspired by the phenomenon that human eyes pay more attention to objects that produce significant dynamic changes, we design a Spatiotemporal Sensitivity Module (SSM) and an adaptive Temporal Activation Controller (TAC). Through these two modules, our framework can mimic the response of the human eyes in dynamic environments by selectively activating the temporal attention mechanism based on the relative dynamics of event data, thereby effectively conserving computational resources. In addition, the integration of a lightweight, multi-scale Linear Vision Transformer (LViT) markedly enhances processing efficiency. Our research proposes a fully event-driven approach, effectively exploiting the temporal precision of event data and optimising the allocation of computational resources by intelligently distinguishing the dynamics within the event data. The framework provides a lightweight, fast, accurate, and fully event-based solution for object detection tasks in complex dynamic environments, demonstrating significant practicality and potential for application.