The collections that open for one day a year
Not secrecy — insurance, stairs, and a collector in their eighties.
A surprising number of serious private collections are viewable, once a year, by appointment, to whoever thinks to write. The barrier is almost never a desire for secrecy.
It is that the collection lives on the second floor of a house with a narrow staircase, that the insurance is written for private use, and that showing people round takes a whole day of someone's life.
Write in autumn, be specific about what you want to see, and offer to come alone. The letters that get answered are the ones that make the visit small.