Possibly, although based on mine, I wouldn't really call that much of a vibration, just a buzz or hum. I'm wondering if you are right about the starter not meshing properly, so it can't turn.......and although I haven't actually looked at the Ducati starter thoroughly, I assume there is a pinion on the end of the starter shaft...... .....I have had cars where the teeth of the starter pinion have worn / sheared, which makes a terrible noise and vibration as the starter turns, but I get the impression from the OP his starter isn't turning at all.
Al One man's 'buzz' is another man's 'vibe's' I too have had cars, where the starter has refused to mesh on one area of the flywheel, but no problem as soon as another area is presented .
Another thought. Stalled mine one night halfway through a ride at a junction. Similar thing - no button, no starter, fuel pump OK. NO spare fuses either. Rescue by van back home. When we checked next day, all connections were good but we cleaned them anyway. Put 12v direct to the starter motor, it worked fine. Removed covers and commutator was black. Rub round with mild abrasive (scotchbrite I think), slipped the brushes out and did the same. It worked fine then, it was just a dirty set of internals that finally would not conduct elecktrickery stuff.....cost £0.
Do you have an immobiliser? But Im not too sure which part of the circuit it protects when the ignition is on.
