Red Light is a painting of David Hockney that he painted before he become a Regular to climb the Tower. The whole painting was stolen by Hell Joe after Hockney refused to help him to find another thorn fragment.
The reason of why David Hockney entered the tower was entirely to find this painting. He traveled and visited many secret auction places that is only open for regulars. He finally find the painting long after he become a regular. However, the painting was ripped into six pieces, so Hockney had to bought it back one piece at a time.
When Hockney finally bought the last piece of his painting, at some point he lost contact with the delivery person. Later he found out from Emile that the last piece of his painting is hidden on the Hell Express. Hockney didn't know exactly where it is, but he plan on staying at the train until he find the painting.
Turns out, Ha Yura is the one who had been using the Emile and had been in contact the whole time with Hockney. And because Hockney introduced his background profile via Emile, Ha Yura quickly find out that Hockney is from Floor of Death, so she wanted to use Hockney to get there. When White asked Yura what if Hockney refuses to help, Yura then replied that she have his "soul" (Hockney refer the last piece of the painting that pictured the red light as his own soul).
Before becoming a Regular, the young boy David Hockney lived in Floor of Death. Together with Yuliu Mata, Hockney was once subordinates of Hell Joe. Unlike Hockney, Mata was tasked only to guard the outside entrance of Floor of Death as "the parasites". While, Hockney had become one of Joe's loyal subordinates. One day, Mata receive an order and mission from the higher-ups to take Hockney and carry him around inside Mata's giant leech and look for the thorn fragment. While both of them traveling around, Hockney told Mata about his dream to leave the floor of death and take journey to the outside world with friends and draw pictures. Hockney and Mata ended up finding the thorn fragment, but after they saw it, Hockney become sort of strange. According to Mata, Hockney said that the painting which he had drawn there contained his own soul. In the end, Hockney went to see Joe and said that he won't help Joe anymore. Hell Joe got extremely angry, plucked out Hockney's real eyes and stole the painting.