I would like a widget that would display in a panel showing a calendar. Imagine 6 months next to each other in a panel at the bottom of the page. For dates that are contained in the data, the number of the day on the calendar would be highlighted in some way. If you click on the given date, it would select all features with that date. Oppositely, if you click on features on the map, it would select the date on the calendar. The calendar would be bound to the time-enabled layer and you could click on either one to explore the other.
My use case is showing upcoming household hazardous waste dropoff events spatially and temporally, so people can choose the event that works best for them.