BEIT SHEMESH, Israel — The carved stone block is about the size of an occasional table. It has held its secrets for two millenniums. Whoever engraved its enigmatic symbols was apparently depicting the ancient Jewish temples. But what makes the stone such a rare find in biblical archaeology, according to scholars, is that when it was carved, the Second Temple still stood in Jerusalem for the carver to see. The stone is a kind of ancient snapshot. And it is upending some long-held scholarly assumptions about ancient synagogues and their relationship with the Temple, a center of Jewish pilgrimage and...