Parameter-efficient fine-tuning (PEFT) aims to adapt pretrained models with a small trainable parameter subset, however, most existing methods choose this subset from fixed architectural heuristics rather than using dynamic, task-aware criteria. We introduce \textbf{FisherAdapTune}, a Fisher-guided Adaptive Fine-Tuning framework that progressively selects parameter groups by tracking the temporal drift of their Fisher geometry. Starting from a PAC-Bayesian view of fine-tuning, we decompose the generalization error bound into Fisher-weighted update costs and show that parameter groups whose curvature contribution has stabilized can be frozen to reduce the error bound without interrupting the remaining adaptation dynamics. FisherAdapTune formulates this criterion with a scale-invariant Jensen-Shannon distance between consecutive Fisher distributions, yielding an adaptive active parameter set. We evaluate our approach on a downstream segmentation task, and results show FisherAdapTune improves the in-distribution performance and zero-shot transfer in multiple settings, validating that Fisher structural drift is a useful signal for efficient, task-aware adaptation. We release our \href{https://github.com/AtlasAnalyticsLab/FisherAdapTune}{code} publicly to enable further application of our proposed approach.