I have just booked a night in the Viaduct so I asked them about the visitors berth and this was their reply:
"The visitor berth is available for a maximum of 2 hours at a time and is free to use. We don’t take bookings for this; you just need to radio VHF73 on your arrival to the marina and they can advise if it is vacant. Our visitor berth is located next to the tidal steps underneath the Wynyard Crossing lifting bridge on your right-hand side. You’re welcome to use it "