You've only given us a narrow slice of what you're doing. In particular I would like to see the full formula(s) on the main page that references the cell on the other tabs that are linked to checkboxes.
I think you need something like this, which is simpler than what it looks like you have now:
If the box is checked the cell will be TRUE, and the IF will take the TRUE option. If the box is checked then unchecked, the cell will be FALSE and the IF will take the FALSE option. If the box has never been touched, the cell will be empty and the IF will also take the FALSE option.
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