Precession paces 20 NAHPs over 800kyr matching proxy data. Eccentricity controls NAHP amplitude through ice sheet extent. Glacial ice sheets suppress humid periods at precession minima causing skipped beats. Ice-albedo cooling dominates suppression mechanism over topography or SSTs. CO2 concentrations do not impact NAHP timing or amplitude. West African Monsoon strengthens and shifts north during NAHPs. Vegetation proliferates to 18N with forests and grasslands in western Sahara. Model underestimates precipitation in northeast Sahara and Arabia. High-latitude glacials control low-latitude Sahara humidity. Obliquity weakly influences NAHPs intermittently. NAHPs enable out-of-Africa plant animal human dispersal. Skipped beats coincide exactly with glacial periods. Precession minima always increase precipitation even if suppressed. Eccentricity signal emerges only with ice sheet forcing. Model accurately simulates Holocene NAHP greening.