Forecasting aurora borealis visibility matters for space weather research and aurora tourism. Visibility at a site and night depends on two distinct factors: (1) whether aurora is physically occurring, driven by solar wind-magnetosphere coupling, and (2) whether observing conditions allow naked-eye detection, mainly cloud cover and lunar illumination. We present Aurora Hunter, a two-stage cascade that decouples these factors. Stage 1 predicts P(occurring) with XGBoost using 51 physics-driven features trained on joint Tromso+Kiruna data (about 16,600 hourly samples, 2015-2023) with labels from the Tromso AI all-sky image classifier. Stage 2 predicts P(clear observation given occurring) with logistic regression using 21 cloud-cover and lunar-illumination features trained only on aurora-occurring hours. The cascade P(visible)=P(occurring)*P(clear|occurring) reaches ROC-AUC 0.937 (Tromso test, 2019-2020) and 0.905 (independent Kiruna, 2024), improving a single-stage baseline by +0.087. Held-out Skibotn data (2022-2025) confirm cross-site generalization. SHAP identifies the Kp x nightside interaction, MLT position, and auroral oval distance as dominant predictors (39% combined). Prototype: https://aurora-hunter.onrender.com.