If my memory is correct, you could have two types of patrol objectives with GFO:
1. A star with a binocular symbol indicates that you need to patrol the area for a certain amount of time. The patrol area is defined as a circle of radius 100nm (usually; there are a couple of exceptions where the radius is 50nm) and you have to remain within this circle until the time is up. Even if you sink zero ships, the objective will complete.
2. A star with a flag icon will turn grey when you approach it and a new objective of sinking enemy shipping will be given. You will need to sink (iirc) 10,000t of enemy ships to complete this. You do not have to sink the tonnage in the vicinity of the objective; you could have the flag in the Solomons but sink all the ships off Japan and it would still be counted.
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