Temporal knowledge graphs (TKGs) have shown promise for reasoning tasks by incorporating a temporal dimension to represent how facts evolve over time. However, existing TKG reasoning (TKGR) models lack explainability due to their black-box nature. Recent work has attempted to address this through customized model architectures that generate reasoning paths, but these recent approaches have limited generalizability and provide sparse explanatory output. To enable interpretability for most TKGR models, we propose GradXKG, a novel two-stage gradient-based approach for explaining Relational Graph Convolution Network (RGCN)-based TKGR models. First, a Grad-CAM-inspired RGCN explainer tracks gradients to quantify each node's contribution across timesteps in an efficient "explain-per-use" fashion. Second, an integrated gradients explainer consolidates importance scores for RGCN outputs, extending compatibility across diverse TKGR architectures based on RGCN. Together, the two explainers highlight the most critical nodes at each timestep for a given prediction. Our extensive experiments demonstrated that, by leveraging gradient information, GradXKG provides insightful explanations grounded in the model's logic in a timely manner for most RGCN-based TKGR models. This helps address the lack of interpretability in existing TKGR models and provides a universal explanation approach applicable across various models.