In the vapor-cell atomic clock, long-term stability can be influenced by slow variations in the discharge lamp's output via the light-shift effect. Additionally, over a multi-year mission lifetime the lamp's aging can degrade its optical pumping efficiency. Understanding the mechanism(s) that drives these changes is particularly important for spacecraft devices, where the atomic clocks are called upon to function continuously and reliably for many years. Here, we consider the two well-known, but little studied, modes associated with alkali rf-discharge lamp operation: the ring mode and the red mode. Consistent with previous research, we find that the ring mode is best for optical pumping, and that the clock-signal amplitude degrades significantly when the lamp operates in the red mode. Examining the emission spectrum as the lamp transitions between these two modes, we show that the ring-mode to redmode transition is driven by radiation trapping within the lamp.