The best hours are roughly 21:00–01:00, when the sky is fully dark and aurora activity tends to peak around local midnight. That is why our tours pick up from Reykjavik hotels around 21:00 — it puts you under a dark sky exactly when the odds are highest.
Arriving too early means fighting twilight; the aurora can appear from about 20:00 in deep winter but is most reliable in that four-hour midnight window. Bright moonlight washes out only faint aurora, not strong displays — clear skies and solar activity matter far more than the moon phase.