How long can the stop in a stop-and-go be?
The AIM covers this briefly (bolded the important part) but effectively you cant sit there very long: 


  4−3−22. Option Approach
  
  The “Cleared for the Option” procedure will permit an instructor,
  flight examiner or pilot the option to make a touch−and−go, low
  approach, missed approach, stop−and−go, or full stop landing. This
  procedure can be very beneficial in a training situation in that
  neither the student pilot nor examinee would know what maneuver would
  be accomplished. The pilot should make a request for this procedure
  passing the final approach fix inbound on an instrument approach or
  entering downwind for a VFR traffic pattern. After ATC approval of
  the option, the pilot should inform ATC as soon as possible of any
  delay on the runway during their stop-and-go or full stop landing.
  The advantages of this procedure as a training aid are that it enables
  an instructor or examiner to obtain the reaction of a trainee or
  examinee under changing conditions, the pilot would not have to
  discontinue an approach in the middle of the procedure due to student
  error or pilot proficiency requirements, and finally it allows more
  flexibility and economy in training programs. This procedure will only
  be used at those locations with an operational control tower and will
  be subject to ATC approval.


The way I read that is effectively you come to a stop and get going as soon as possible. If you intend on doing anything else you should inform ATC. I take this to be a time limit of, as soon as you stop, get going again.