I was previously confused about classical vibrato and thought that you were supposed to roll your finger higher and lower within the fret and it magically worked to change the sound even though it is not a fretless instrument. My vibrato was weak when doing this though!

The true objective is to use a "can shaking" motion of the shoulder to push and pull the string further or closer to the bridge, adding or decreasing string tension. The effect is that it ends up looking similar to the violin vibrato but it is in fact different! I tried this and could instantly hear the effect was way more pronounced than the rolling I used to do since I actually knew what I was trying to do!

Hope this helps! below is how I came to understand the technique properly:

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Here is a good vid on vibrato!

https://www.youtube.com/watch?v=BLCxmF-Xgyk

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Here is a good explanation about what you are trying to accomplish physically:

https://music.stackexchange.com/a/32314

"Start by giving yourself the most advantage:

• Location on a string: Start with all your fingers fretting notes on the same string in the middle of the neck. The closer to the 12th fret you are, the more it is possible to move the note.
• String selection: Start with a string where you can get a good grip on the string (a wound string). I recommend the 4th string, so that you don't have to reach more than necessary.
• Use all your fingers at first: for example put your first finger on the 7th fret, your second on the eighth fret, your third on the ninth fret, your fourth on the tenth fret of the same string. Push and pull with all fingers gripping the string.

Now move your hand towards the bridge and the nut, back and fourth with the goal of grabbing the string and pushing and pulling it with all your fingers working as a team. In other words: move your arm which moves your hand which moves your fingers which stretches and relaxes the string tension. You should be able to produce a quite pronounced vibrato effect where the pitch moves both higher and lower than the true fretted pitch. You will be able to discern a pitch change without a tuner. As you get more and more comfortable with this technique, try it with less and less fingers, and in less ideal conditions (Such as on an unwound string, or closer to the nut). I commonly contrive to use two fingers, even though mastering the use of the single index finger is quite possible. In actual performance, I continue to take advantage of using more than one finger, when the fingering suggests using a finger that is not my first as the optimal choice.

Note that this vibrato technique often looks just like the improper technique of simply rolling your finger. If you play a stringed instrument such as the violin, that is exactly how to do vibrato, but this does not work on fretted instruments.

Also, you can get a quite pronounced effect with this technique. Sometimes the desired effect is more subtle, so once you master the technique in practice, understand that you often can and sometimes should do less in performance.

Also, the clarity of effect seems to be less pronounced on older strings for what ever reason." - almagamate

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May your practice be relaxing and fufilling!