You had the pass made on the guy in front of you and you let him back by you in the next left turn after the straight. My advice is that most passes ( with the skill levels being close to the same) are made in the braking zone. Everyone accelerates out of the turns on to the straights fairly equally. Be confident in your ability to make the turn, brake later than the other guy and set up for the turn on the inside of the guy you are passing. And then make it stick through and after the turn.
Be confident enough in your own ability to be assertive and look out for opportunity. Passing "on demand" is hard when you are similar speed, so be thinking about the next couple corners and figure out where I good place to pass would be.
Lots of places in that video you could've been a little later on the brakes and taken the inside line.
The way I understand it is that's not him in the video on the onboard bike. I recognize the name, Ty Howard...pretty sure he has or had multiple track records in TX and kicked a lot of ass in CMRA. He'd likely be faster than anyone on this forum. I'm guessing is he's working with the guy with the number shirt on that's why he wasn't passing, and OP is just using the video as an example of "passing on demand".
Anyway, the comments I wanted to make is first of all...it's a track day. If you're not sure that you can make a pass safely and you have to ask yourself that, then don't do it! Let the guy in front go until you know for sure you can make a safe pass. In a race it would be a different situation...people are more aggressive in racing because every position, and ever pass matters, so it's a different mentality but for a track day, my advice would be to think safety first.
With that said, IMO, passing strategy is one of the most difficult skills to get good at. Everyone goes through the same thing you are and the smaller the difference in pace and skill between you and the guy you're trying to pass, the harder it is to do. It all boils down to confidence in yourself, and trust in the other person. Need confidence to tell yourself that you can make this pass without crashing or doing something stupid, and you can make it stick. Need trust in the other person that he won't do something unpredictable right at the last moment when you're making the pass. That's why everyone always tells beginners to BE PREDICTABLE in your riding, so that you won't screw up the people trying to pass you and cause an accident.
I won't say that I'm amazing at passing others, but in the last 2 years I have gotten significantly better at that even though my pace only improved by a few seconds generally. And I'll tell you exactly what really helped me with that....RACING! It doesn't make much sense and it's hard to explain, but 99% of it is a mental game. During track days I was always either too scared or generous and didn't want to take much risk so I was always getting stuck behind people. But as soon as I started racing, something in my head just clicked and my mindset changed to "Don't give a fuck, I'm going to pass this guy because 6th place sounds better than 7th place!"
And I'll be damned, it fucking worked! lol....on top of that, I also had a hell of a lot more opportunities to pass people because there are more people grouped up on the grid at the start rather than at a track day where everyone is spread out more, so I quickly gained more experience in passing people in places and at times that I normally wouldn't. I started making passes that I used to think were sketchy but now I realized there's nothing really sketchy about them, I'm just getting a bit closer to the other person. The way I look at it now is if we don't touch, all is well, regardless of whether I'm the one making the pass or someone else is passing me. The downside to this is once you gain that experience, you need to remember to tone it down when you're at a track day. At my last track day this year I was a bit of a dick to other people because I was riding like that without realizing that those people were probably not too fond of my passing since they were less experienced and skilled and not racers. After that sessions I reflected upon it and realized that if I was in their shoes I'd probably think "wow that guy is a dick", so I toned it down after that. But I remember being on my little 500 and passing 5 guys in 3 corners, going around outside of a guy, inside of 2 other guys in the next turn then around outside of 2 more guys riding on the exit curb and even clipping the grass and going off the track by a few inches. That's when I realized, I shouldn't be doing that. Now in a race...all fair game
I think I have a couple of videos from some MRA races if you're interested to see, that show more passing aggressiveness on my part because I started every race on the back row and had to make my way around some people.