Swamped

Perhaps you can get the subject onto boating, and use that to bring up what happened to you. Then they might be more inclined to volunteer how they ended up here.

"What do you usually draw, then?"

"Whatever I see that looks interestin'. There's folk who like to draw things they think up in their heads, but I ain't got the imagination for that."

"Any favorites? I doubt you can show them to me right now, but I'd be interested in hearing about them."

"My best work's portaits. If I can get someone to sit still long enough to draw 'em." They smirk a little. "Don't suppose you'd be interested when they let us out of here?"

You think you might be able to work with this.

"I'm leaving tomorrow, but I'm not expecting to be in town long after that. Though admittedly, since the whole reason I'm here is that my boat sank, I'm not entirely sure when I'll have a way back."

"Well, you're not gonna be hiring any boats out until after the holy day celebrations," the patient replies. "And they'd damn well better let me out before then."

"Oh, is it an important day for you?"

"Don't get me wrong. The gods ain't done much for me, but at a party like this, everyone likes a good drink. Especially the sailors. That means a winery makes a good bit of extra money. Which means those of us workin' to make sure there's enough wine to sell get a nice bonus. So I'm really hopin' to get out soon. 'Course, it'd help if I could get some sleep now."

Well, this seems like a chance to move the subject where you want it.

"They haven't told you how long you'll be here?"

There's a pause.

"They say it depends on how I look tomorrow. Definitely won't be able to do any of the heavy lifting if I get back to work, but there's plenty of easier stuff I can still do."

You try to look as befuddled as you can, since you really shouldn't already know the injuries.

"Is it that hard to know how long the injury will need?" Of course, you know it is. You may not have been a doctor, but you heard them talk about that sort of thing often enough.

"Well, there's always some people who heal sooner and some people who heal later. They do think the weird mark over my heart's gonna be there for a while, but it doesn't actually hurt, so who gives a crap. The other side's where they figure things could go bad."

"Mark?"

"Some madman came rushing at me with a sword and a hot poker. Got no clue what he wanted. Never gonna forget his face, though." They shudder a little. "Got a real good look at it. I'd wager I could even draw it from memory, and I hardly ever do that. 'Course, I ain't gonna find out, seein' as I still ain't got anythin' to draw with."

Well, there's blank paper and pencils in the records room. Not to mention some swampleaf to help them sleep. That would take valuable time, but their attacker might just be the believer you're looking for. So it seems worth the risk.

The problem is, it's not as if you can just say "well, if I get you drawing tools and a sleep aid, will you let me keep a picture of your attacker?" That's going to seem extremely strange, if not downright suspicious. You'll have to lead the conversation a bit to get there without coming across as too odd.