A change of course after at sea docking would indicate a possible new command or "piracy to steel a ship". If there is a ship of interest to the Navy, they will conduct reconnasaince to watch it regardless.
Update:
S Korea finds no al Qaeda evidence on cargo ship
31 October 2003
KUNSAN: South Korea said on Friday it had found nothing unusual on a Greek-owned ship after an investigation sparked by a tip-off it could be carrying members of Osama bin Laden's al Qaeda group.
"Joint investigation agencies have searched the ship for weapons or forged passports but have not found anything unusual," an official at Kunsan port told Reuters by telephone.
"There will be no more big investigation like yesterday's but we will keep watching the ship until they leave the country," said the port authority official, who declined to be identified.
Meanwhile New Zealand customs today said it would not reveal why the ship that visited New Zealand was subjected to top-level-security checks saying the information is "sensitive".
http://www.stuff.co.nz/stuff/0,2106,2711582a12,00.html If the ship really was given a clean bill of health, why do they still have to keep watching it, until it leaves?