Mockingbirds typically sing throughout the day and night. Singing is driven mostly by personality, so they sing at night for the same basic reason they sing during the day. Unmated males tend to sing more during the night, but they also sing more in general than mated birds.
The Cornell Lab of Ornithology indicates that mockingbirds sing more at night during a full moon. This extra singing may result from the brighter lighting that draws out more personality from the birds. Female mockingbirds often sing more in the fall for territorial purposes. The darkness of night comes sooner in the United States during fall months.