Your description of hours of operation reminded me of a Paris, France Catholic Bakery I read about in the New Yorker. The author of a food column traveled there to judge this bakery for his column, but when he arrived it was always closed. Finally, after repeated visits he learned that a hole opened in the convent wall at 2 AM. His source told him to Be There. Indeed, at 2 sharp a hole opened and in 30 minutes they were sold out and the hole closed. I don't recall what he thought of their product.