Recall Knowledge: Impossible Information

Hi all! Relatively new GM to Pf2e. Running a campaign right now where the party is uncovering clues regarding the upcoming reveal of an obscure and ancient enemy.

As the party is encountering these clues, they are trying to glean information using recall knowledge that would be, in my mind, impossible to recall.

For example, they found the banner of the ancient enemy and tried to recall information to know who the banner belongs to. The ancient enemy has not been seen for generations and only 1 person in the whole town has any knowledge of this enemy but chooses to keep quiet.

My question is what would be the way to handle this? I opted to let them do the recall knowledge but the DC was the normal DC for their level +10 for the extreme difficulty.

Ultimately they failed the checks and gained no information, but should they have even rolled? Or should I have simply said this isn't something they could possibly know about?

Looking for advice or any existing rules for this I suppose and hope I'm posting in the right place! Thanks!

You of course can declare some information inaccessible, especially in such cases.
Generally people would recommend giving useful information on Recall Knowledge about creatures in combat when PC spend actions on it.
Outside of combat it's mostly your judgement based on common sense. Also published adventures sometimes tell what to say on some specific RK checks.

I agree that if players spend actions in combat (combat and more generally when time/rounds are being tracked) then they deserve to get some benefit for having done so, assuming they can meet the check. And in such a circumstance setting the check too high is a bit unfair. But it's also not difficult to come up with something that the players could learn. You could have a thousand year old mummy that the players know nothing about as far as history, but during the fight they can still figure out that it has vulnerability to fire.

Anyways, in the case of an out of combat check, I would consider it fair to say something like, "You have no knowledge on this topic, except that it's related to X town/country. You should look for people or books that might provide more information on the subject."

If no one has heard of this thing for 2000 years, you should expect not to know much without more serious investigation being done.

The simplest way to handle this would be to roll the check for the players as by RAW it is a secret check, and then just tell them "you don't know anything" regardless of what they roll. Rolling openly has the danger of a nat 20 and players being upset when that doesn't matter. Setting an impossible DC has the danger of critical failures being likely, and if people know nothing then feeding them a bunch of false information isn't particularly plausible and will probably distract from the actual plot.

I agree with them though I'll add that not all Recall Knowledge is recalled knowledge. Some of it is deduction, as mentioned with the in-combat examples of analyzing one's enemy. Some of it can be negative, like in "I know what it's not" or in which gaps in history it might fit and so forth, indirect. And as Claxon gave an example, sometimes it's knowing the next step in the dark toward figuring it out.

But there is a point when the high-level PC's abilities can become nearly magical or Sherlock Holmes-ian, well beyond anything realistic in our world. Whether it's through connections to cosmic forces, muses, deities of knowledge, or whatnot, they simply can (and to a degree are expected to) know the unknowable. The two main ways to handle proficiency gating are to either require a minimal proficiency in the Recall Knowledge skill (this is called "proficiency gating") or use such a high DC that rolling a 20 still doesn't achieve success (that is until PCs have leveled up a lot). Since Recall Knowledge skills are typically Secret, players just go with what they get either way, and even if they do land a 20/crit success against all odds, that doesn't impart any degree of certainty (or at least not any more than earlier crit fails might have).

The original Rise of the Runelords had such hidden lore, with DCs in the 40s (maybe even 50 IIRC) that the PCs could only really recover via adventuring, though the later PF1 adventures set the same DCs about 20 lower due to the success of those first adventurers unearthing it.

This is definitely a situation where there is no one right or wrong way to handle it, and will depend largely on your party and you and whether the party needs a narrative push in a specific direction or not.

For narrative/plot recalls:

I like allowing rolls on very difficult checks. I have players with dubious knowledge and so they usually know that they either failed or critically succeeded if they get 2 pieces of information, or they critically failed or succeeded, and got one piece of information. I like that both always include a good and bad option.

When the party critically fails, my first course of action, depending upon how much they need the information to advance the story, is to point them in the right direct for all the wrong reasons. If I know that there is a spy in a local community that is hiding in the local religious site, I might give them a clue that the banner has something to do with that god, or a noble family that it really doesn't, then have a new encounter with the potential source that they can get where they need to go eventually. Or if they really don't need the information yet, I will connect it to something that is coming up way down the road in the adventure, usually in an implausible context, so they kind of suspect I just made something up entirely, but if anyone takes note of it, down the road they might be prepared for undead cyclopses or magma dragons to eventually make their way into the story.