Clothing: While these NPCs are played as hidden influences, not much visual contact should be made. Perhaps a glimpse of a purple cloak, possibly a gleam from a golden circlet. Most often they will just see a figure hidden within the shadows, a person peeking through the curtains or nothing at all.
Face and Body: Not much before they are actually met, in which case they would mostly be played in a more straightforward manner. Excessive fat, abnormal height, immense muscles, etc. would probably be noticable (if the PCs were to see the hidden influence from afar).
Desired outwards appereance: Obviously the PCs will probably not realize who the hidden influence is. Their beloved aunt Magda might be the mysterious head of the alchemist guild, but to them she is just “Aunt Magda with the greatest pancakes in the world”. The strange man they spoke to at the market might be their arch nemesis, and they would not even know it. Hidden influences might be known by name, but only the darkest rumours would hint at their true agenda.
Most often the PCs won’t even meet the hidden influence, not until they reveal his identity and come to end his wicked ways.
Area of Effect: Hidden influences are detected through their area of effect. When the benevolent King suddenly pass restrictive and authoritarian laws, it might be the work of a hidden influence. When the PCs discover a murdered noble in the library, the receding shadow in the doorway might be the hidden influence. While the real murderer might go to jail, the hidden influence was the manipulator who arranged the death. (Through guile, money, blackmail or something else) The PCs might (for instance) discover that there is a hidden influence when they discover a “mysterious letter” in a book belonging to the murderer.
Sixth Sense: I use the sixth sense alot when I want to give the players a clue that something is amiss. A note to a player telling him “he has a bad feeling about this” or that “he feels someone watching them”, are easy ways to do this. Combined with the glimpse of a person “emerging from the shadows to whisper in the kings ear”, would work perfectly as they exit the throneroom.