I've been teaching myself to play some classical pieces on my nylon string guitar and want to improve my vibrato technique; specifically when holding several notes.
I'm referring to the technique of applying vibrato by stretching the string along its length rather than side to side.
I've been using the piece "Romance" (AKA 'Romanza' or 'Romance d'amour', etc), from Book 2 of Ben Bolt's '39 progressive solos for classical guitar', as a study for this purpose. Here it is played beautifully by Peo Kindgren ->
In the sections where there are arpeggios on open strings with melody played on the first string I can apply the vibrato quite nicely, but in the trickier sections I struggle to achieve any vibrato at all.
I've had some success by thinking in terms of shaking my thumb on the back of the neck as opposed to shaking my fingers, but it doesn't come naturally.
So I'm looking for general advice on technique and/or specific exercises to help develop this aspect of my playing.
Conclusion: I have accepted the answer from @amalgamate for the insight that the movement should originate from the arm muscles. This is exactly the information i was looking for.