THE SHORT ANSWER
March is the best month. We see the strongest aurora of the year in March, consistently, every season. September and October are a close second — clear skies, active lights, and good driving conditions.
That said: your odds are good whatever month you pick. We average around 20 departures a month and see the northern lights on roughly 95% of them — across the whole season, not just the best months. When the sky is covered above Rovaniemi we drive. Sometimes a few dozen kilometres, sometimes several hundred, crossing into Sweden or Norway if that's where the opening is. We don't give up on a night because one spot is cloudy.
It all comes down to luck in the end. Cloud cover varies enormously year to year — some Marches are wide open every night, others we barely manage ten departures because it barely clears. Come with a few nights available and the odds are strongly in your favour.