I have seen some unsuccessful attempts at vibrato with a remarkable amount of jaw movement but with very little change in the sound itself.
I have seen other players get a beautiful vibrato with little or no visible movement of the embouchure. What's going on here?
For the unsuccessful attempts, it's almost as if the center of the embouchure is actively resisting all physical movements and firmly "locking on" to that steady sound.
For some reason, this reminds me of the "rubber pencil" magic trick. Maybe some of of you have done this trick before. If not, stop and try it now. Here's a video that may help...
The key here is to...
Focus on the pencil, not your hand.
When attempting vibrato, perhaps the key is to...
Focus on the vibrato, not your embouchure.
Visualize the center of the embouchure as supple, pliable...not rigid or tense. Focus your attention on the controlled wavering of the sound, not the mechanism that creates it.
For mid-range notes some find it helpful to think of "woe-woe-woe-woe." For higher notes (with the partials closer together), I prefer to think of "ya-ya-ya-ya." But neither of these is literally what I'm doing. I arrived at those vocal sounds after the fact, not as a means of figuring out the vibrato in the first place.
If you have ever watered a garden with a hose, perhaps you spent some time making patterns in the stream of water by shaking the hose. This also reminds of me of vibrato. I'll bet when you were making those patterns, you weren't focused on the arm holding the hose but rather on the patterns in the water itself.
Same idea as the rubber pencil...