Some interesting points raised here but possibly a legal minefield.
The captain must be the one who signs the tech log. If its the instructor then he is the captain and the pilot under check must put it in his logbook as something other than P1. Notwithstanding flybymikes comment in post #2, P1/s is possibly the most appropriate.
If the pilot under check is the captain then the instructor is merely a passenger and has no legal right to interfere with the controls. Now imagine the scenario where the pilot under check has made a complete pigs ear of the flight so far and the instructor, sorry passenger, has severe doubts about the rest of the flight being made safely. I would suggest that instinct of self preservation would bring the passenger to utter the words " I have control". I'm no lawyer but I would suspect that at this point technically an offence would have been committed. Which one I'm not sure (piracy? hi-jacking?). If this leads to a disagreement between who has control and subsequently leads to an accident then I would suggest that the "no win no fee" parasites would have a field day. Possibly the insurance would be invalidated.
If you are an instructor would you want to be put into this position. Probably not so either you are the captain or you refuse to do the flight. The latter may not go down too well with some employers.