And since, despite the world's admitted tendency towards situations best left in the more dramatic varieties of literature, it wasn't literally a stereotypical gothic novel, Kanimir didn't expect anything in particular to happen. If nothing else, there were far more storms that happened to happen at night than there were potentially literature-worthy shenanigans. So it's completely reasonable for him to be curled up in his grand library, enjoying a book on magical theory.
Then she can happily spend a long time reading (and get hungry and retreat to her room to eat a snack and then go back to reading).
After an...amount of time...Kanimir finds her again. (It's probably been at least a few days, maybe a week.) "I think I might have something--an avenue of research, not a potential spell," he clarifies. "But I think it would help to see you doing your kind of magic again, under slightly different circumstances." He holds out a book. It's magicked to tell him when it's been read, and how much and what specifically. "Can you read this only in your selfspace?"
Riya nods. "Yes, I can do that."
Her inner self takes the reflection of the book from Kanimir's reflected hand and opens it.
After he's recorded what he wants to record, he examines the crystals closely, frowning. "The fact that you were reading the book didn't register at all," he reports.
"Your kind of magic works in a fundamentally different way from mine, so far as I can tell, but after extended poking and prodding I've been able to compare its transport function to some magic with similar results from here. I...think that if I could get an appropriate spell drawn up, I could use some of the information entangled with the door's residue to target where you came from."
"And, in case we needed it--we have confirmation that you are from very, very far away. If I'm making any sense of what I'm detangling, you're from farther away than Fairyland, along the same axis."
"It has a better chance of helping than anything else that readily comes to mind."
"Perhaps it would be useful to show you some relevantly magical things, and see what your method of detection gets out of them."