Despite the absence of artificial light pollution at Antarctic plateau sites such as Dome A, other factors such as airglow, aurorae, and extended periods of twilight have the potential to adversely affect optical observations. We present a statistical analysis of the airglow and aurorae at Dome A using spectroscopic data from Nigel, an optical/near-IR spectrometer operating in the 300-850 nm range. These data complement photometric images from Gattini, a wide-field (90 degrees) CCD camera with B, V, and R filters, allowing the background sky brightness to be disentangled from the various airglow and auroral emission lines. The median auroral contribution to the B, V, and R photometric bands is found to be 22.9, 23.4, and 23.0 mag arcsec(-2), respectively. Auroral emissions most frequently occur between 10-23 hr local time, when up to 50% of observations are above airglow-level intensities. While infrequent, the strongest emissions detected occurred in the hours just prior to magnetic midnight. We are also able to quantify the amount of annual dark time available as a function of wavelength, as well as in the standard BV R photometric bands. On average, twilight ends when the Sun reaches a zenith distance of 102.6 degrees.