The room isn't designed for long-term human occupation. There is no bathroom, no food, no bed, no climate control - though this is Florida, so climate control is not such a concern - no plumbing.
But there's lots of magic. It's such fun to make, after all.
(Nathan had been worried he'd have to ask one of the succubi, or Joham, for lessons on what might whimsically be called "safe sex". He likes not having to bother with this better.)
"You're a sweetheart," he says. "Don't go killing people for me, it'll just make Goldie mad."
"With luck, there will never be anyone quite that accessible who I want to kill for you."
"But if you don't want me to kill such people, at least point them out so I can report them to Her Majesty and get them blacklisted from immortality?" Nathan asks hopefully. "Then we can just outlive them."
"I wanna get a place," the Joker declares. "Stick around for a while. Get a sewing machine. Make pretty clothes. What do you think?"
"Sure," says Nathan. "If you have someplace in mind I can come up with when to ask about obtaining it."
Wandering - and possibly more ducking into alleys, as alleys present themselves - ensues!
The Joker, it turns out, is naturally attracted to small, crappy apartments on the lower floors of small, crappy buildings.
"...Babe, you know my shiny gold credit card and the account connected to it could get us a nice place, even in Manhattan, right?"
"None of the amenities common to nice places really make a difference to me, but I'm puzzled about why you don't."
"I suppose magic can cover for whatever's wrong with any place we wind up with as long as we hide the non-Euclidean storage space when the landlord drops by. But - landlord sounds annoying, let's get a condo, let's own the place, not have to negotiate to be able to paint or put in a picture window or whatever."
It is harder to find a decent condo than a crappy apartment; it takes longer. But the Joker doesn't mind much.
The best time to ask about this decent condo over here is in forty-five minutes. That's enough time to scandalize that stray alley cat over there, isn't it?
Nathan's timer didn't fail them: they're desperate to sell the place and let him bypass the background check after he offers to put a payment down on the spot.
They could christen every room in their condo. Purely for celebratory purposes. Yes.