Model simulates 20 NAHPs over past 800kyr matching proxy timings. Precession minima pace all NAHPs via intensified West African Monsoon. Glacial ice sheets suppress NAHP amplitude during 17 precession minima causing skipped beats. Eccentricity indirectly forces NAHPs by controlling ice sheet extent. CO2 concentrations do not impact NAHP timing or amplitude. Ice sheet albedo change cools atmosphere weakening monsoon and jets. Vegetation proliferates to 18N during NAHPs with forests and grasslands. Western Sahara sees highest precipitation increases up to 763mm/yr. Northeast Sahara and Arabia show weaker model response than proxies. Obliquity influences NAHPs secondarily to precession and eccentricity. High-latitude glaciation controls low-latitude Sahara humidity. NAHPs enable plant animal and human dispersal out of Africa. Model improvements from palaeo-conditioning better simulate Holocene greening. Snapshot simulations validate against dust wax and sapropel proxies. Ice sheets reduce meridional temperature gradient inhibiting convection.