Supposing the player established for me that they (speaking as character) were determined not to give up the information. And I, as DM, have established that this is the Queen's Own Supreme Torturer we are speaking of, who has brought a thousand traitors to confess their villainy, notwithstanding that each was equally determined not to spill. I'm going with - outcome uncertain
This is actually an interesting case study, imo.
My go-to question is: how can we make this "real", rather than pretend? That is, similar to the idea of asking how do we
actually make the player worry that this orc is a threat to their 10th level barbarian?
One way, which admittedly would be problematic for a
bunch of reasons, would be to make clear to the player that this guy is actually going to cause their character permanent injury, resulting in reductions in attributes and maybe other penalties.
"Ok, reduce your Strength score by 1. Willing to talk now?"
"No!"
"Ok, another point off Charisma. How about now?"
"No!"
"Next step is going to be difficulty speaking, which means any spellcasting with verbal components will have a chance of failing. Keep going?"
"Umm.....will I be able to undo all this with magical healing?"
"Hard to know until you try."
I'm not actually advocating that approach, but if you want a realistic "Queen's Own Supreme Torturer" that's how you do it. That's immersion.
I have zero interest in playing a game in which the DM rolls dice and says, "Yeah, he is
super scary." And I say, "Oooh....I'm terrified! Ok, I'll talk!"
I mean, in some sense I don't even have to respond. The DM could just narrate (while I eat Doritos), "Yup, he got a 23. So, you give up the information, and then what happens is...."