The commonest use of Zhang Guolao in ordinary religious life has little to do with his stories. He is petitioned for sons, and the standard image of him, printed and hung at weddings, shows him mounted and presenting an infant to a couple.
How an aged hermit became the bringer of children is not fully explained by anything in the narrative material, and the tradition does not appear to have felt the need. Popular cult attaches functions to figures for reasons that are often iconographic rather than narrative: an old man of enormous longevity is an auspicious presence at the beginning of a family line, and the picture works whether or not a story supports it.
The tests he is put through in the fuller accounts are of a piece with the group's humour. Summoned to court, he is served poisoned wine to see what he is, drinks it, falls asleep, and wakes complaining only that his teeth have gone black; he then knocks them out and grows a new set. Offered an imperial princess in marriage he refuses and vanishes. When the emperor sends a man to fetch him again he dies on the spot, is buried, and the coffin is found empty.
The Eight Immortals appear together far more often than singly, in the eight-crossing-the-sea story and on birthday and New Year decoration, and Zhang Guolao's mule is usually how a viewer picks the group out of a crowded design.