When do blinking lights become just plain annoying?

The zeners should be connected in series, back-to-back. That combination is then put in parallel with the bulb. This will clamp the bulb voltage to the zener voltage plus the "forward voltage" of the other zener (~0.7V). If the two zeners were individually connected in parallel, facing opposite directions, then neither zener would conduct in the zener region and bulb voltage would be clamped to 0.7V (approximately).