To light the fire in Beast of Reincarnation, and thus complete the "Origin of the Ringing" quest, you must take a long walk through the Pilgrim's Zone, have a chat with one of the rusted golems, and uncover a hidden clue. The fire puzzle is one of the few obstacles in Beast of Reincarnation that can't be removed by the blade, but once you've figured it out, the next Nushi fight won't be far away.