I think some used Mountain Shadows, Sun Dials and Hour Glasses.
There are certain flowers that only bloom at night or under Moonlight. These include the Evening Primrose. Moonflowers as well. Moonflowers stay open all night and close when the first rays of sunlight touch their petals. Many Night Blooms have a heavy fragrance to help moths and other insects find them, such as Night Gladiolus and the very expensive Casablanca Lily.
Greek and Romans had rather precise water clocks in all major cities, A horn would be sounded at each hour or a gong struck. The Roman Calendar used in the time of Jesus was based on the Egyptian and was solar. Israel was a bit behind the times. Julies Caesar had changed the Roman Calendar (with a little help from Cleopatra) The day was divided into 12 hours—each one for the 12 Gods. But the daylight hours were longer in the summer and shorter at winter—but they always had 12 hours of day and 12 of night. Still time was only on the hour— :I shall meet you at the Temple of Jupiter at Mars”.