The term "Night Battle" is used to describe intimate physical relations between a human and a KAN-SEN. The term was first used by the YouTuber Doujingod78 in his video detailing the legality of sleeping with a ship girl from the popular Japanese gacha game "Azur Lane."
The video in question concluded that it was indeed very illegal to have physical relations with a ship girl.
Takao: Where have you been going on Wednesday nights Atago? Its beginning to affect your abiltiy to attend training on time.
Atago: Oh, I have been training Takao. The Commander has been gracious enough to engage with me in some Night Battles, hehe~