If you can hear what someone is doing, chances are you can teach yourself to imitate it. It is counterproductive to count the pulses of your vibrato when you are playing after you have learned to control the speed. Doing it this way is too cold, analytical, and scientific. Using vibrato has to do with warmth, emotion, and life itself. Think instead of the emotional content of the music.
Passionate music demands a fast, deep vibrato.
On the other hand, mysterious music might use a very shallow, quick vibrato. Something that is more lyrical requires a slower, shallow vibrato. Know the rules of musical syntax. Music is a language just like English, French and Swahili. For starters, there are strong and weak beats in a measure with the first beat always the strongest unless displaced by an accent.