We study on-device time-series analysis for gait detection in Parkinson's disease (PD) from short windows of triaxial acceleration, targeting resource-constrained wearables and edge nodes. We compare magnitude thresholding to three 1D CNNs for time-series analysis: a literature baseline (separable convolutions) and two ultra-light models - one purely separable and one with residual connections. Using the BioStampRC21 dataset, 2 s windows at 30 Hz, and subject-independent leave-one-subject-out (LOSO) validation on 16 PwPD with chest-worn IMUs, our residual separable model (Model 2, 533 params) attains PR-AUC = 94.5%, F1 = 91.2%, MCC = 89.4%, matching or surpassing the baseline (5,552 params; PR-AUC = 93.7%, F1 = 90.5%, MCC = 88.5%) with approximately 10x fewer parameters. The smallest model (Model 1, 305 params) reaches PR-AUC = 94.0%, F1 = 91.0%, MCC = 89.1%. Thresholding obtains high recall (89.0%) but low precision (76.5%), yielding many false positives and high inter-subject variance. Sensor-position analysis (train-on-all) shows chest and thighs are most reliable; forearms degrade precision/recall due to non-gait arm motion; naive fusion of all sites does not outperform the best single site. Both compact CNNs execute within tight memory/latency budgets on STM32-class MCUs (sub-10 ms on low-power boards), enabling on-sensor gating of transmission/storage. Overall, ultra-light separable CNNs provide a superior accuracy-efficiency-generalization trade-off to fixed thresholds for wearable PD gait detection and underscore the value of tailored time-series models for edge deployment.