When to start tapering?

Gary, taper from what?  Tapering is a bit of an art form which is to address the balance of stress and recovery. I would imagine that you will do OK with a three day taper.  Just don't go extreme during the week or so before the race.  For the triathlon it is way more complex than an ordinary single event.  There is the combined fatigue and the individual sport fatigue.  Individual event is pretty easy, though the taper time may be substantially different for each sport.  Running tends to take much longer than cycling or swimming.  If I am at high mileage running it may take two weeks, maybe one week for cycling, maybe three days for swimming.  Do no to overthink it; it is not as important as the training itself.  A three day taper will work for most, longer only if you have really built up.

OK, thanks. I am mainly concerned about the running.

The purpose of a taper is to allow the benefits of prior training to be fully utilized on race day.  The more stressful the prior training, the more of a taper you will need.  How long that taper is will depend on your fitness level and the load factor of the training you did before the event.  The harder you train, the more taper is recommended.  If you feel like you can train hard and be completely ready for another training session in 48 hours, I would probably taper at least 72 hours for an upcoming race.  Personally, I will do one or two really short bricks in the two or three days prior just to put my body through the transitions from one sport to another while keeping the intensity factor very low (think Z1 & Z2 HR).  No more than that though.  Not only that, you get a chance to practice transitions.  'Real' training sessions are pretty much over with on Monday or Tuesday before the weekend of the race.

FWIW,
Greg