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You don't move them day to night.
There are two underground camp configurations. You use the Day/Night toggle button to select the underground configuration that you want to work on. Let's say Night. Then you move camp equipment back and forth between Inventory and the Underground Camp.
Same for Day. You use the Day/Night toggle button to select the underground configuration that you want to work on. Then you move camp equipment back and forth between Inventory and the Underground Camp.
A piece of camp equipment can be either Camp configuration, or neither, or both.
Before you purchase Camp Equipment, make sure you have used the Day/Night toggle and selected the camp configuration that you want to put the new piece of equipment in.