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Everytime Nagato blinks she feels an emotion.
Because she is a human interface she was not designed to be fully human, however she has the capacity to adopt human like features. That is why she starts to have emotions as a result of her interactions with the other members of the brigade. In other words, the more she interacts with others the more human she becomes.
You can see that at the beginning of the series she is completely emotionless but as the interactions start and develop she blinks more often.
The alternative version of Nagato from Disappearance should not be considered, because she is already a normal girl.
Nagato's emotional development is a mark of her personal growth along the series. However, the more human like she becomes the more faults / errors will accumulate in her, because humans are imperfect beings. Slowly, as the series progresses she distance herself from the entity who created her and thus faults start to multiply, but also her genuineness develops along her personal growth.
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