Final answer:
The key trait for successors in the era of sage rulers was the virtue of heeding and applying divine wisdom for societal benefit, exemplified by filial piety and devotion to work. They were akin to 'philosopher-kings', serving the greater good and managing their realm effectively.
Step-by-step explanation:
The most important trait for a successor to have during the reign of the sage rulers, based on Chinese philosophical traditions such as Confucianism and Mohism, was the ability to listen and respond to divine insights—connecting with spiritual wisdom to benefit society. This quality is depicted by the Confucian philosopher Mencius through exemplars of sage rulers like Shun, who showed exceptional filial piety and selfless devotion to work. Additionally, these rulers demonstrated political acumen by managing and spreading their influence, as seen with King Ashoka's patronage of Buddhism. Being a philosopher-king, akin to the Platonic ideal, emphasized the importance of serving the greater good and aligning with the Mandate of Heaven, while showcasing virtues such as loyalty, devotion, and the skillful management of both practical affairs and prestige goods.