Robust feature encoding constitutes the foundation of UAV tracking by enabling the nuanced perception of target appearance and motion, thereby playing a pivotal role in ensuring reliable tracking. However, existing feature encoding methods often overlook critical illumination and viewpoint cues, which are essential for robust perception under challenging nighttime conditions, leading to degraded tracking performance. To overcome the above limitation, this work proposes a dual prompt-driven feature encoding method that integrates prompt-conditioned feature adaptation and context-aware prompt evolution to promote domain-invariant feature encoding. Specifically, the pyramid illumination prompter is proposed to extract multi-scale frequency-aware illumination prompts. %The dynamic viewpoint prompter adapts the sampling to different viewpoints, enabling the tracker to learn view-invariant features. The dynamic viewpoint prompter modulates deformable convolution offsets to accommodate viewpoint variations, enabling the tracker to learn view-invariant features. Extensive experiments validate the effectiveness of the proposed dual prompt-driven tracker (DPTracker) in tackling nighttime UAV tracking. Ablation studies highlight the contribution of each component in DPTracker. Real-world tests under diverse nighttime UAV tracking scenarios further demonstrate the robustness and practical utility. The code and demo videos are available at https://github.com/yiheng-wang-duke/DPTracker.