Well, run this by your teacher. This is how I learned. (Not liminal—I’m her partner using her account, at her request!)
Never forget, the motion starts all the way back at the elbow.
Sit in playing position with your instrument. You can put your bow down and rest your bow hand on your right knee. Raise your left hand into a playing position, placing your 2nd finger (middle finger) on the D string somewhere in the vicinity of 2nd position. Say, on about a G natural. With a motion that originates from your elbow, and without depressing the string, move your second finger slowly back to about an E, then up to about a B flat. (so, between approximately ½ position to 4th position) The exact notes don’t matter. Keeping your 2nd finger at a constant nearly right angle to the string, just like your normal playing position, move back and forth in a relaxed fashion between the two positions. Feel your elbow really contributing and propelling the motion. Once you get the feel of that, and your speed between the two positions is about 1 second for a round trip, then your ready for part 2.
Gently and gradually narrow your range of motion (so, start moving between about an F natural and an A, then an F# and an A, the F# and G#, etc.) As you narrow your range of motion imagine the pad of your 2d finger getting sticky ever so gradually. Start depressing the string, again very gradually, as you narrow your range of motion. Likewise, increase your speed gradually, though keep it comfortable and relaxed always. (Speed is not the point!) As you your finger pad gets stickier and the string begins to depress, start converging back on the G vicinity where you started. When the exercise comes to the last stage, the string will be depressed fully as if you are actually playing the note, your elbow will still be propelling and managing your motion, but since you are now “landed” you will feel the tip of your finger bone riding back and forth on the pad of your finger which is itself in contact with the string and the neck.
Now you will start to notice the way the mass of your hand is actually a factor in the motion in a way that probably it is not for the violin (not sure—I do not play the violin). Sitting on that G-ish note, you should have a lot of motion originating still back from the elbow and manifesting in your hand which is moving rather rapidly now in an almost vertical fashion. The difference is that now all this motion is “tethered” at a single point on the string.
Final point: In a mature vibrato, your knuckles should not be rotating, primarily, but rather moving parallel to the neck of the cello just like it was before when you were exaggerating between ½ and 4th position. If your emphasis is on a rotation-like motion, like tipping a bottle, then probably you’ve taken your elbow out of the effort and are trying to manage the motion from your wrist.
There are some more nuances that I don’t think I can describe here in words, but if you can get the feel of that motion then you will be well on your way! Then start practicing with the weaker fingers on other strings.
Good luck! And please, run this by your teacher.