What 'dark enough' means
The aurora is there in summer too, but it's faint next to a sky lit by a sun only a few degrees below the horizon. You need the sun more than about 12° down before the sky is dark enough for the colours to show.
The best months
September to March. The longest nights are from November to January. Around the equinoxes, in September–October and March, the aurora tends to be more active, and September and October nights are milder than winter's. Cloud is the real obstacle: watch the cloud forecast, not just the aurora activity.
What summer gives you instead
Light all night: midnight hikes, golden light at 11 pm and puffins on the cliffs until late. Plan your aurora hunt for a later trip, from late August onwards.