I believe the reason no one is sharing their personal observations is that they do not believe or want to make assumptions about a single act triggering coyote dispersal, myself included. Based on my observations, I don’t think there is a specific moment when the alpha gathers the group for a ritualistic act triggering dispersal. Instead, I believe the young coyotes gradually start to separate as they age, venturing out in small groups or alone until they eventually do not return. They form hierarchies and bonds, which can influence certain littermates to stay longer.
Just because you cannot see or hear coyotes doesn't mean they aren't present. I have hunted them extensively using greyhounds. Typically, six or seven trucks will surround a one-mile section of land; Oklahoma is flatter than Iowa. Hunters on all sides of the section communicate with CBs and use binoculars, often able to see the opposite trucks a mile away. It takes something significant to get a lot of those coyotes on their feet so they can be seen—like sending in bloodhounds, having someone go into the area, or even shooting.
When local farmers tell me they haven't been seeing coyotes, that doesn't discourage me from hunting in that area. If I observed what you described and then patrolled the area 24/7 using thermal imaging, I wouldn't feel confident making an assumption that those coyotes have left the area just because I hadn't seen them again.
I have observed a lot of coyote behavior and social interactions, primarily at night when they are most active, using thermal imaging. During the day, they tend to layup, and most of their activities occur after dark. Wild animals, like coyotes, do not follow consistent patterns throughout the year.
It's important to note that male coyotes only produce sperm once a year, testosterone has no affect on their sisters' decisions to disperse. This factor alone scientifically disproves the group would disperse at once. Often, during the breeding season, I call in pairs, only to find two males with pearly white teeth. I feel confident making assumptions like they are brothers, in their first year of producing sperm.
Considering all these factors and my experiences in the field, I do not believe there is a single moment or ritual during which all the young coyotes disperse at once.