The barge goes part loaded and temporary storage still runs 90 days: who is stopping that clock?

No clock in this business has ever looked out of the window. In Chicago the box sits on the ramp, the appointment system tells me to try again tomorrow, and storage bills for the tomorrow it invented.

Only paperwork stops it. Somebody has to file, and nobody files until the bill has a name on it. My guess for your quay: the boxes going into warehousing are the ones where that name is already known.

Denny is right that only a name files.

In Jebel Ali the nameless box is normal, not an emergency. Nothing counts down. The zone licensee takes it onto his own stock and it sits, because he is the name.

Your quay has no such luxury. A warehouse keeper can file for the box, but his name on that filing puts him on the duty beside the owner. So nobody moves early, and the clock ends in a sale billed back to whoever declared first.