I shall enter the fray with some trepidation as I have not officially gone to Instructor school yet. I have been pressed into duty as an instructor but only with intermediate students unfamiliar with a track or wanting a second or umpteenth opinion of where they might improve (fresh set of eyes and all that)
I drive a slow (by track standards 116whp) car and therefore whether its required or not find myself doing alot of point bys and have to really pay attention to my mirrors.
I progressed through the NASA HPDE program up to 3/4 and found value in the point by passing only in the straights novice class. When a student first starts they have enough on their plate just learning their car and the track. It often falls to the instructor to watch the mirrors and traffic while the novice learns how to drive again. I do not like the idea of relying on your instructor to tell you who is behind you or when to point but sadly in happens alot. I reccomend getting the student to do their own traffic management as soon as possible.
I have had all kinds of instructors over the years from the guys who I could hear speaking to me without a chatter bio to the guy who only could use hand signals because his chatter box broke. I was not very successful as a student using only hand signals. I was too busy driving and watching the mirrors to pay attention to the emphatic and un-recognizable hand gyrations going on next to me. In his defense he was very soft spoken and needed his chatter box to instruct. I had an instructor grab my steering wheel going into Turn 1 Road Atl because he was conviced "we" could turn in sharper. He was a little off as my street tires did not messure up to his expectations. Lucky for "us" we just slid out to the far gators without incident. I did not like it one dang bit and he didn't do it again. He learned that I did in fact know the limits of my car. It's not always the case but sometimes the student does know what the car is capable of.
A few bullet points I have learned from experience on track and from lengthy discussions with instructors.
Don't give up on having an instructor just becuase you are being promoted to a solo group. Having an experienced driver ride second seat will almost always help your driving improve.
If you don't click with your instructor/student talk to them about it and if needed make a change swap instructors/students. It can save your track weekend.
Listen to your instructor he/she was put in your car for a reason and it wasn't to hear how fast you think you are and how much you don't need their help.
Breathe, relax your hands a little, breathe, stay calm, keep your eyes up and ahead of where you are, and Breathe.
If there is a car in your mirror for more than a few seconds he did not magically appear there he is faster than you let him by whether that means a mandatory point by or a politewave/point by to tell them you know they are there and aware they are going to pass you.
If possible Watch said faster car/driver to see if you can learn why they are faster than you
Ride with your instructor/ take your student out in your car to show them what you are teaching them.
I could go on and on.