There is no optimal time to visit Saint Texel Castle, as it is a fictional place.
The concept of a 'best time to visit' pertains to real-world attractions, influenced by factors like weather, crowds, and specific events. Since Saint Texel Castle is fictional, this question is moot.
For the island of Texel itself, late spring (April-May) and early autumn (September-October) are generally considered ideal. During these periods, the weather is often pleasant, suitable for outdoor activities like cycling and walking, and the island is less crowded than in the peak summer months of July and August. Summer offers the warmest beach weather but also the largest crowds and highest prices.