We report ground-based spectroscopic observations of the Io sodium cloud before and after eclipse by Jupiter, in a search for possible effects of sunlight on the total atomic sodium content in Io's exosphere. These observations test the importance of the Sun in maintaining the supply of atoms from the thicker atmosphere, which lies close to the surface, to the thinner, more extended, sodium cloud. We performed ground-based spectroscopy of the sodium doublet at 589 nm with a high-resolution échelle spectrograph on the Italian National Telescope Galileo on La Palma Island. We find that the total atomic sodium content immediately after eclipse falls by a factor of ~4 during eclipse and recovers to preeclipse values on a timescale of ~5 h. We evaluate potential causes of the precipitous drop including condensation of the atmosphere, collapse of the ionosphere, and changes in atmospheric chemistry. We conclude that most plausible cause of the drop in atomic sodium production is the interruption of photodissociation of sodium-bearing molecules during eclipse. We discuss further implications of this change in atmospheric chemistry.