Issue with date format change while reindexing

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Please update your post.

Here you set that you read from person.birthDate and write to timestamp but you did not change or remove person.birthDate which is still incorrect.

You should use the _simulate API to see exactly what you are doing before run the reindex operation.
And it's probably not as straightforward as you think it is. The date processor helps to parse a string and make it a date. It does not help to render the field with the format you wish AFAIK.

But why do you want to change the date format after all? Could you explain it?
Is that for display purpose? Can 't you solve that at render time? I mean that a date is a date in elasticsearch whatever its format in the _source document.

If it's about inserting data, then your field can support multiple formats. See https://www.elastic.co/guide/en/elasticsearch/reference/master/date.html#multiple-date-formats. In which case you don't even need to reindex the data.