Turns out, when I went to sign up for the advanced group for this track day, it was sold out. But, there was one instructor spot left, which meant I could run in the advanced group when I was not instructing. A lot of the guys I knew from NASA instructed, so I figured I'd give it a try.
I had been invited to instruct for NASA by their lead instructor for over a year, but hadn't taken him up on it for two reasons: 1) they don't want you to race and instruct, so I'd have to only do TT, and 2) cars don't have dual controls (like airplanes do) so if things go wrong, I can't take control. That has a couple of implications: 1) you can't demonstrate how something should be done and then let the student do it, and 2) if something goes terribly wrong, you also can't take control. In addition, no one ever arrives at a flight lesson saying "I know how to fly - I've been doing it for years." Not so with driving.
I was paired with someone who had never been on the track before. Per some advice from the more senior instructors from NASA, the first couple of sessions, I focused him on looking ahead, and finding not only the entry cones, but the apex and exit cones for all turns where they were visible. It was amazing to see the difference when he didn't do that. It's easy to get overwhelmed when you are trying to think about acceleration, what's the right gear, where should I be on the track, and... oh, yeah... driving. So, this focuses them on driving first, and all that other stuff is secondary.
In the third session, the lead instructor for Group A pulled in front to do a lead-follow. We only were able to do that for about half a lap, and then got separated by traffic. So, the start of the fourth session, we pre-arranged to do a lead-follow for a couple of laps. It really helped him for the remainder of the fourth session.
As is often the case, he was tired and opted not to go out on track for his last session. OK with me. I get to start packing up earlier to head home.