The only requirement, having worked out which peak is the higher, is that the activation zone cannot include land that is connected to that peak via a dip of more than the activation zone definition (25m in vk, maybe 80ft in USA?)
Put another way, if you travel on the most elevated path from the highest peak to the lower one, the point where that path first dips below the higher peak by any more than the 25m (or 80ft) defines the outer border of the activation zone.
So if the dip between the two peaks is only say 24m then the lower peak would be included in the activation zone. If it's more than 25m/80ft then the lower peak is just a parking area.
The horizontal separation does not matter.
This is based on my understanding of the prominence rules. Subject to being overruled by a more elevated authority.
73 Andrew VK1DA/VK2UH
AM for vk2