According to what I've read, you're supposed to get this quest from Bartholomew after saving him from several trolls.

How does one trigger that?
When I visit him before the troll invasion starts, there are no events on the map. If I visit him afterwards, I can ask him about the fire immunity, which causes the "discovering troll in the basement" sequence (which is supposed to come later than the troll attack from what I've read?) but no quest.

Can't edit the title, but it's called "Guiding Beacon".

The way I got it was to save him from the trolls in his basement and at that time agree to find his whip.

I think it triggered when I looted the troll bodies. This was last week and I've stopped playing since then, sorry.