In human conversation, empathic dialogue requires nuanced temporal cues indicating whether the conversational partner is paying attention. This type of "active listening" is overlooked in the design of Conversational Agents (CAs), which use the same pacing for one conversation. To model the temporal cues in human conversation, we need CAs that dynamically adjust response pacing according to user input. We qualitatively analyzed ten cases of active listening to distill five context-aware pacing strategies: Reflective Silence, Facilitative Silence, Empathic Silence, Holding Space, and Immediate Response. In a between-subjects study (N=50) with two conversational scenarios (relationship and career-support), the context-aware agent scored higher than static-pacing control on perceived human-likeness, smoothness, and interactivity, supporting deeper self-disclosure and higher engagement. In the career support scenario, the CA yielded higher perceived listening quality and affective trust. This work shows how insights from human conversation like context-aware pacing can empower the design of more empathic human-AI communication.