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My wife is working part-time/casual worker in the school. This is not a full time employment
and will only be working when needed.
Is it fine to include this information in additional information sheet. I am not sure as this is
temporary work it can be mentioned in Occupation details in the Good Character section

Her occupation is whatever her job title is at her job. The Home Office isn't concerned with the type of contract (e.g. casual, permanent, full-time, etc.). You just need to disclose what she does for a living/her occupation.