I did not see that episode of H.I., but the paint technique is a very simple one. With base color, preferably eggshell already painted, you can then *wash* on a top color. It can be lighter, as the one you saw, or it can be darker. You can even just lighten the base color w/white.

Mix the glaze (paint + glaze + water) and apply with a brush, just skimming the top surface, keeping most of it out of the grooves. Hold the brush more on an angle, say a putty knife, with a side to side movement, or the letter X. (It's all in the wrist).
Or, brush on and wipe off with a rag.

Practice right on the wall for technique, and once you've confirmed color/technique, just paint over it. And, I think it's safe to work in short intervals with this technique. Meaning you won't see where you stopped and started.
Good luck!!

Thanks for the encouragement. It sounds feasible, even for me.

Is there a specific ratio of paint:glaze:water that works best? Also, should the new paint be in an eggshell finish as well?

I'm not usually so timid about starting a project, but the room and adjoining hall total about 500 SF so I know it's going to take me a long time to complete. The idea of botching it and needing to do it over has kept me from starting. However, with these 100+ temps I am not doing any work outside so I may as well get going on the painting.

It looks like this episode will be re-aired on August 28 at 8:30 am E/P

The paint/glaze ratio will ultimately depend on the color you want. The more paint, the more opaque the glaze. It's, again, trial and error, but not difficult.
Ideally, both paints should be at least an eggshell finish. Not to complicate things, but a glaze can be made with just paint and water. Nothing wrong with doing it that way!
The eggshell finish for the base coat is so that the next layer sits on top, and not absorbed.
Start with a 50/50 glaze to paint in a bucket, then add water to make the mixture more viscous. Add water a little at a time. The mixture should be creamy. Too watery and it will run. Not enough water may just tire you out a little sooner.
Again, this is not difficult, but you will need patience. Do a sample on the wall and let it dry.

Nosoccermom, thanks for checking the schedule. I didn't realize that the episodes are aired more than once, so I'll set the TiVO to catch it. There's a long list of jobs that I can tackle in the meantime.

Paintergirl94, thanks again. I had to pick up some Peel Bond for another project at the SW store so I bought glaze, too. Being patient is not one of my strong points, but maybe this will help me practice.

How you put the paint on is going to determine the look you get just as much as the paint. As someone else posted you can use a brush but there are other options too. I did a glaze in one room and used one of DH's old t-shirts cut up into strips and tied together. I lightly dipped the shirt in the paint and rolled it on the wall. You can even use a plastic bag or a bunched up piece of paper.
I'd strongly suggest finding a scrap of cardboard or lumber to practice on to see what instrument and glaze mix works best for you.

Yes, patience is probably the worst part! I've been doing decorative painting for a loooong time, and I still find myself rushing the process. At times, I literally watch paint dry (as I put my finger and thumb in the shape of an L on my forehead). If you're waiting on a small section of paint to dry, you can use a hairdryer.
Rag-rolling is another option for application, but, IMO, since your walls are already textured, it may be a lot of extra work.
Do you know what colors you'll be using?

Glazing, sponging and ragging are not easier than just repainting in the color of your choice. Trying to get an even texture with top coat is far more difficult than just putting on a 100% opaque layer of paint.

Been there, done that.

You choose decorative painting because it's a look you enjoy, not because it's easier. It a LOT harder than a simple paint job. If you just want an easy room refresh, nothing beats a plain coat of paint. If you like the accenting of the texture, then a decorative finish can do that for you, but it will come at a cost to your patience and time. It's much more time intensive and difficult than a pro makes it look on TV. No, it's not constructing a super collider, but if you have health issues, this will tax them much more than rolling on paint. Especially your knees, arms, and upper shoulders.