I to had the same problem with my Brise, 18 months old and the click returned intermittently...if I pressed the starter button repeatedly it would start.
Phoned Tim at Brise and he sent me a new solenoid the following morning, fitted it problem sorted.
However looking at the two the old plunger seemed to be sticking abit compared to new one, so try rubbing it down with some crocus paper light coating of grease and refit before ordering a new one, which is about £50 delivered