While dawn or sunset or moonrise are possible, you would have two man-made options for party time. You could specify a time based on a sundial, or a water-clock. The sundial would be more likely: even a simple one could be made, the gnomon just a rod mounted in a sunlit wall, the dial just a mark on the wall to indicate noon. Of course, there has to be sun, for a sundial to work. For the night, there was a water-clock.

The water-clock or clepsydra could also be simple, often just a pot of water with a controlled drip into another pot, with marks on the side. They could be useful and reasonably accurate as timers for tasks, but as clocks they had to be periodically re-filled and calibrated- which meant setting them to a sundial. Various novel elaborate water-clocks were made in the ancient world, fitted with mechanical visual devices or alarms. They were still never very accurate, which is why they could be replaced by even simple geared clocks in the medieval period.

It is not surprising that Andronicus of Cyrrhus would have both sundials and clepsydras on his famous Tower of the Winds, so that the time could be seen both day and night. He also made the tower high enough to be seen from the agora, making it an early example of a clock tower. Precision in a clock was for most purposes not as important as just having a public timepiece, something that everyone in the town could see or hear to regulate their days.