One option.
You could add a hook to points along the curve (select a point then Ctrl+H / Hook to New Object) and then animate the hook z location with a noise modifier to give random movement
I don’t want a cycle of vibration, I want to start it, stop it, then start it and stop it once more, but at specific times which aren’t going to be cyclical. Such as On at 100, Off at 600. Then On at 900 and Off again at 1700. So there’s no time frame that’s the same.
Sorry, I should have explained better to start with.
Two options spring to mind since you cannot keyframe the influence of the noise modifier.
1: Add a Limit modifier below the noise modifier for each time range you want to stop it
2: Add a limit location constraint to each hook and set the Z location you want the hook to stop at, then keyframe the constraint influence value to turn on/off the constraint. Constraint off = noise modifier works, constraint off = noise modifier off
Each option applies to one hook in the attached file