There are a handful of away-from-the-instrument exercises that brass musicians can do to help build embouchure strength, such as free buzzing, the pencil trick, jaw retention drill, and the P.E.T.E. These exercises, when done correctly, will help players target specific muscles used for playing without the risk of excessive mouthpiece pressure. I’ve recently come across a similar exercise, explained by George Rawlin. He calls it the “bull dog” exercise.
I have a couple of minor issues with some of the things he describes in his video. At one point he talks about the “ideal set” for a player’s jaw to be protruded forward so the teeth are aligned. This is correct for a large number of players, but some brass musicians actually play better with a receded jaw position. Embouchure characteristics like this depend on the player’s anatomy and you shouldn’t try to force your jaw to a position that doesn’t work for you. His discussion about where the mouthpiece gets placed also doesn’t apply to all players. His bit at the end about “air play” and relying on the instrument to get the buzz may be a good playing sensation to go after for some players, there are other players who need to go after the opposite sensation and work on firming up their lip center more.
I don’t feel that the position of the mouth corners when performing this bull dog exercise is necessarily exactly how you want to play, but it does at least seem to work on the muscles at the mouth corners where you want to focus your effort. If done carefully and in moderation it could be helpful for some players who need to strengthen up the muscles that intersect at and just under the mouth corners.