Please don’t. We’ve all had wonderful teachers who have said this to us at times. I don’t think they actually meant it. Vibrating every note is like adding sugar to everything you eat. EVERYTHING! Usually, the vibrato is singled out when someone is vibrating only certain fingers in only certain positions. If that is happening, either the vibrato is coming from the wrong place in the arm/hand or the hand is not balanced. The ideal is to be able to vibrato on every note and then choose when and how you want to color the phrase with it. OK, so let’s go back to some basics.
Considering at the basic vibrato motion, try this exercise. It’s something for cellists just learning how to vibrate but is also useful to come back to as a refresher. Find 1st position on any string. With your thumb anchored on the neck and your fingers lightly touching the string, do a very wide vibrato motion. Let your fingers slide up and down the string concentrating on the motion of your arm. I like to focus on the place about two inches back from your wrist. This is something that can also be done away from the instrument using your right arm to substitute for the neck of the cello. (Good for late night TV reruns)
More to come...