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Yes there is such an exception:
For children under the age of 18 who have not received booster shots (third doses) or do not obtain vaccination certificates, if they are accompanied by a guardian with a valid vaccination certificate and who will supervise the children, they will be regarded as holders of valid vaccination certificates, as an exception.
If children under the age of 18 without holding vaccination certificates enter Japan by themselves (without being accompanied by a guardian with a valid vaccination certificate), they are not eligible for the above exception.
If you think about it, if there was no such exception, those with children that can't get the booster shot can't enter Japan with their children! :(