Here's a basic example of the sort of situation I have in mind: the scene is a meeting with the PC's contact about their current quest progress. You've described the scene in that context and telegraphed anything you thought was relevant. The scene goes as you expect. At the end of the scene, before the contact leaves, a player makes the following action declaration: "I want to know if the contact knows anything about [issue related to one of the PCs' other quests], but I doubt they'd tell me if they did. So I'll bring up the topic in conversation and watch their body language to see if they startle or otherwise look uncomfortable when I mention it."
The DM can't have telegraphed yet anything related to this new issue, because it wasn't part of the scene until the character brought it up. So the approach "watch their body language to see if they startle or look uncomfortable" can't be tied to something unique about the situation provided by the DM's description.
You said such a generic action declaration at your table is impermissible, so if this sort of player-initiated action is possible at your table, how would it work? Or is there some other aspect of play at your table that makes the example inapplicable?
Again, you seem to have a flawed idea of what my game looks like. Your second paragraph is very odd to me, and doesn't look like my game at all. I don't prepare specific telegraphs to guide players in my game. I, instead, make sure I show the things that indicate things, like a lying NPC having clear tells, or an odd gouge in the floor in front of that door perhaps indicating a trap. If the players don't engage this NPC or door, I don't provide a telegraph.
So, when the player engages the NPC on a topic where I know the NPC is lying or hiding something, that's where a telegraph might appear based on what's currently happening in the fiction. It's not a scripted thing where I can be suddenly caught off-guard without a prepared telegraph -- that doesn't sound like anything in my game at all. The gouge in the floor above would be because I know there's a scythe trap in the ceiling above the door, and so such a gouge makes sense. The telegraph follows the fiction, especially in social encounters.
So, to address your point, I'm not sure how this would come up in my game. If there's an NPC that the PCs think is hiding important information from them, I'll know if this is true or not. And, I'll have a sketch of the NPC at least -- mannerisms, traits, flaws, maybe a bond -- enough to extemporize any encounter with the NPC. So, to start with, if this NPC has important knowledge, I don't see how that wouldn't be expected to be addressed. If they didn't, the above is super easy -- they'd appear confused at the sudden turn and say they don't know anything. No roll would be asked for, as this is what happens.
IF they did know, well, I'm not going to be caught by surprise on this. This kind of trick is, in my opinion, excellent play and not a generic action. They PC has lulled the NPC with non-dangerous discussion and has sprung a surprise question to elicit a response. I'd need to know what the danger level of the information was, and why this NPC would try to hide it to fully adjudicate the response, but I'd likely call for a CHA check to set up the bait-and-switch ploy. A success would realize the PC's goal -- they'd confirm this NPC knows something. A failure would result in not confirming the information and would likely alter the interaction to be more hostile to the PCs (down a step on the attitude chart, maybe). Specifics depend on the situation.