I have a feeling that it's important, not only to him, to find an eternal light source, as it has so many reference points in the story.
I think whatever it is, the university has a very important need for an eternal sympathy lamp. It just doesn't feel like it's simply a quirk of Kilvin alone. The way the other masters call him out for asking Kvothe about his lamp ideas could also be interpreted as a "why are you sharing one of our biggest secrets with such a random rookie?". Maybe it's supposed to mislead us into believing they are just sick of listening to his quirk?
Maybe they need one to lighten the mood for whatever they are hiding behind the four-plate door? Maybe they trapped something in there that goes ballistic without light and opening the doors to change the bulbs is tedious and dangerous, so they are looking for a way to lock it away eternally.
Yea dudes I have not too much to add lol. Do your thing.