For me, I was able to start it after I finished the quest "Where is Fina?" then I spoke to the manager afterwards, in the morning/daytime (can't remember which).I've searched through the thread, but I still haven't managed to do it.
How do I trigger the Elizabeth Darkwood quest? Does the spa quest with Finna need to be unfinished? Because the redhead at the spa just greets Krowly during the day, and doesn't let him in during the night.