Professor Kaori glances at me for a heartbeat before looking away. “He attempted to use that power to revive a fallen rider—which didn’t work, because there’s no signet capable of resurrection—and depleted himself in the process. To use a phrase you’ll become accustomed to after Threshing, he burned out and died next to that rider.”
2nd read: Theory- Naolin did not die but became venin because Brennan is NOT dead! So there is no reason for him to try to revive Brennan. Tairn has not said anything regarding his last rider Naolin to Violet so its not entirely unrealistic Naolin wanted to draw more power than Tairn could provide and being venin was the answer to that problem.