First of all, Lighthouses are an attraction. Most of them are not any longer in use. They can be visited from outside only, occasionally from inside. Some of the Lighthouses have a dramatic location, some a touching history and others are simply beautiful.
Texel where the Eierland Lighthouse is located is a year round destination. In summer the lighthouse is open to the public daily. Autumn and winter are less crowded.
You can visit year round, sunset is stunning but lighthouse is open to the public on Wednesdays only from 2 p.m. until 5 p.m.
To beat the crowds visit between arrivals of the ferries. During winter only open on Wednesdays.
Every Friday in July and August you can climb up the stairs between 7-9 p.m. You get the tickets at the boathouse Boulevard Zuid 5. I like it most with dunes infront, so late afternoon until evening is the best light for this picturesque Lighthouse.
Peggy's Point is world famous and very popular. Tour buses and rental cars arrive throughout the day especially in the summer. However, there are two easy ways to beat the crowds even in the peak months:
Be there in the morning as early as possible. At least before 9 AM. Experiencing the sunrise is amazing anyway.
Don't leave before or right after sunset. Just stay! Most visitor leave when the sun goes down, but the place gets even prettier. Check sunrise und sunset times here: Halifax Canada | Sunrise - Sunset
The best light for a good shot is in the morning or at sunset and there are fewer crowds. The opening hours of the lighthouse are from 9 a.m. to 5 p.m. Less crowded during the morning.
Best seasons are late spring, summer, and beginning of autumn (October/November until March). Rain can occur more often in "winter" - the "rainy" season.