Classical guitarists roll the finger for vibrato like a violinist — how does that work on a fretted instrument?

Your analysis of the violin is right and your instinct about the guitar is right too — the sounding length genuinely does not change. The movements look similar and the mechanisms are different.

On a fretted instrument the pitch changes because of tension. The string is stretched between the fret and the bridge. Pressing and rocking the finger changes how much the string is displaced and stretched, and a string under more tension sounds sharper.

So the rolling motion is not moving the stopping point, it is modulating the stretch. That is also why the effect is subtler on a guitar than on a violin, and why it is more effective on higher frets and thinner strings, where a given displacement produces a larger relative change in tension.

One practical note for anyone trying it: on a classical guitar the effect is much stronger above about the fifth fret and nearly useless in the first position.

That is straightforward from the mechanism — near the nut the string is short and already at high tension relative to the displacement you can produce, so rolling achieves very little. Players who feel that their vibrato does not work often have been trying it in exactly the place where the physics is least helpful.

There is a second technique that guitarists use, and the two are often confused because they look different but sound related.

Longitudinal vibrato — the rolling motion along the string, as you described. Modulates tension, gives a gentle vibrato, and is the classical guitar approach.

Lateral vibrato — bending the string sideways across the fingerboard, repeatedly and slightly. This changes tension much more dramatically and is the electric and steel-string approach. It produces a wider, more obvious effect and it only goes sharp, never flat, because you can only add tension.

That asymmetry is worth noting: on a violin, vibrato oscillates around the pitch in both directions. On a guitar it mostly pushes sharp from the fretted note. Good players compensate by aiming slightly under the pitch so the average lands right, which is a genuinely subtle piece of technique.

There is a third contributor that is not about pitch at all, and it explains why guitar vibrato is audible even when the pitch change is very small.

The rocking motion changes how the finger contacts the string and how energy is damped at the stopping point. That modulates timbre and sustain slightly, not just frequency. The ear reads that as expressive movement even where a tuner would barely register a change.

This is a general point about instrumental technique worth holding on to: several things people describe purely as pitch effects are partly timbral, and the two are hard to separate by ear because the ear was never designed to.