A box model of the coupled ocean, atmosphere, sea ice, and land ice climate system is used to study glacial-interglacial oscillations under seasonally and orbitally varying solar forcing. The dominant 100 kyr oscillation in land ice volume has the familiar sawtooth shape of climate proxy records, and to zeroth order, it does not depend on the seasonal and Milankovitch forcing. The sea ice controls, via its albedo and insulating effects, the atmospheric moisture fluxes and precipitation that enable the land ice sheet growth. This control and the rapid growth and melting of the sea ice allow the sea ice to rapidly switch the climate system from a growing ice sheet phase to a retreating ice sheet phase and to shape the oscillation's sawtooth structure. A specific physical mechanism is proposed by which the insolation changes act as a pacemaker, setting the phase of the oscillation by directly controlling summer melting of ice sheets. This mechanism is shown to induce deglaciations during periods of lower summer insolation. Superimposed on the 100 kyr are the linear Milankovitch-forced frequencies of 19, 23, and 41 kyr. The transition from 41 kyr glacial cycles to 100 kyr cycles one million years ago may be explained as being due to the activation of the sea ice switch at that time. This would be the case if sea ice extent was more limited during the warmer climate of the early Pleistocene.