Skip ahead to 1:20 and you will see how a student learned the arm motion for vibrato. He is practicing it by doing the shaking motion with both arms which helped him to get the feel of it. Then he does it with the cello and reinforces it by adding the right arm motion.
Some thoughts on Vibrato
Vibrato is a very personal thing. When I was young, I didn't want to play with vibrato because I felt like I was exposing myself and it would be embarrassing. Eventually, I got over that self-consciousness!
I've given Vibrato it's own place on the menu of this website because although it is a left hand technique, vibrato is an integral dimension of your sound. Through vibrato, you express different shades of feeling so it is very personal.
Once you have the skills to control your vibrato, cultivating your sensitivity to sound and touch will allow you to express your unique self. It takes careful listening to make the sound you want in order to suit the phrase you are playing.
Start listening closely to your vibrato and the vibrato of other cellists playing the same piece. Most students don't listen to their vibrato so you have to really zero in on it.
Another thing is that you might think your vibrato is wider than it actually is. The sound under the ear is different from the sound across the room so record yourself and see if you think your vibrato sounds like what you thought you were producing. Try exaggerating each finger's vibrato to test the limits and decide if you must work a lot harder with 3rd and 4th finger to get them to vibrate as wide as 2nd finger can (maybe first finger too).
Listening closely to other cellists, especially close up in a live recital, will help to wake up your sense of what is possible in terms of expressiveness with vibrato.
I tell my students that they must love their vibrato and that means that the vibrato they've chosen to use in a particular note or phrase must be a genuine choice of their own.
Over time, you will become adept at varying the elements of vibrato which are the speed and the width.
Like everything on the cello, there must be balance in the body and for each finger that does vibrato. Here's a video which talks about noticing tight muscles and other things that could interfere with producing a vibrato.