So if I understand correctly...
A guard walks on the parapet minding his own business. At a 100 feet, down in the field, stands an unhidden invisible monk breathing slowly and watching the guard. All of a sudden, the guard looks toward the monk and says: "I know where you are punk! You'd better be careful!"
Am I the only one that finds this laughable to the extreme?
Or this one
During the Rock Show of Cacophonius the Bard, an invisible Arcane Trickster climb on the stage. The music is loud, very loud with the unique spell Cacophonius invented: "Pump up the volume!" a spell that makes music louder so more people can hear his perfect music. So our invisible arcane trickster climb on the stage but did not take the hide action. Cacophonius stops the show, turns toward the arcane trickster and says: "I know where you are you little autograph stealer! Go back in the crowd or I'll give you to the bouncers!"
By using these silly example, I hope to wake up the logic that people have. Use your logic. Rules are not everything. Especialy when adapting a rule to something it was not meant to rule...
Neither situation deals with combat so there's no Hide action to be taken in your examples (mosh pit notwithstanding). I'd hope the DM at the table would make a reasonable ruling about the invisible character based on the scene and what the player has said the PC is trying to accomplish and how they are going about it.