For distributed control systems, modern latency-critical applications are increasingly demanding real-time guarantees and robustness. Response-time analysis (RTA) is useful for this purpose, as it helps analyze and guarantee timing bounds. However, conventional RTA methods struggle with the state-space explosion problem, especially in non-preemptive systems with release jitter and execution time variations. In this paper, we introduce SAGkit, a Python toolkit that implements the schedule-abstraction graph (SAG) framework. SAGkit novelly enables exact and sustainable RTA of hybrid-triggered jobs by allowing job absence on the SAG basis. Our experiments demonstrate that SAGkit achieves exactness with acceptable runtime and memory overhead. This lightweight toolkit empowers researchers to analyze complex distributed control systems and is open-access for further development.