For me, elbow block was kinda a natural thing. I believe one of the biggest disadvantage from the elbow block, is that you are slow to retaliate/counter with punches. But as Sylvie explains, it's a great tool to mix with elbows.
I tend to have my elbow a bit sideways during the block, covering a bit more the jaws from a straight. I don't like to have it pointing straight out. A bit less chances to hit the fist with the pointy part, but safer.
I was first taught to use the elbow block for high kicks, so that the glove completely covers the head almost to the back, so that the instep wont do damage behind it. But that move stuck with me for the hooks as well, even if no needed. The punch wont reach that back far. And then I started to use it for directs too. It blends very well with the high tight guard, and the long/half long guard that i usually use. When you use a high guard, moving to an elbow block is very fast, you don't even have to recognize the punch before starting the movement. You don't care if its a straight, hook or even a feint. You start your motion and you make the small adjustment on the fly.
For punchers, it may not be the best type, but if you use elbows, and for clinching entries, it's very nice to flow from it.
@AndyMaBobs
For the second video, Muay Thai elbow counters to boxing tutorial, i really don't like this technique for 2 reasons.
-The title of the video has the word boxing in it.
-I really don't like the idea of using 2 hands to block 1 punch with the one hand making a swapping movement. If he feints the strike, your swapping hand will live you badly exposed, probably even for a high kick. It's something i would definitely try to take advantage if my opponent use it like that. I don't know, it just doesn't feel safe for me.