The light bonus appears to change every 2 hours. Was in a party farming Garuda HM and we were getting bright light from 9am to 11am cst. At 11am it changed to gentle light. So we tried Titan HM to see if the bonus moved to there and it did. Starting at 11am Titan HM started giving bright light. We are done now but i would assume Titan HM will give bright until 1pm cst then it will likely change to Moogle HM. And im willing to bet the 2 hours before Garuda it was Ifrit HM.

Id bet it works the same for dungeons too. Just have to figure out the rotation they go in and at what times each one has the bonus.