I am assuming, because you refer to the period for the exercise of public rights, that you are referring to the external auditors. Appointments of external auditors are not made by the parish council but are made on an area basis (unless a council opts out and councils generally don't) by the Smaller Authorities Audit Appointments Ltd. which itself is appointed by the Government. External audit contracts run for a limited period (I think it's five years) for parish councils within the appointed area and those appointments were made, nationally, this year. In my area we have the same audit firm but many will have changed. This would probably have been reported to council but no decisions are required or possible as this is an appointment made externally. Is this the "sleight of hand" you are referring to? The name and the contact details of the external auditors must be displayed on the notice of electors rights within the parish.
The internal auditor is a different matter and must be independent of the parish council but is appointed by the council. It is part of the process to review the work of the internal auditor each year; not just review the report but also consider whether the process is fit for purpose and meets the recommendations of the Joint Practitioners Guide. A resolution of the council is required on the appointment of an internal auditor and whilst most parishes will review that appointment every few years, some will do so more frequently and some less so.
So, going back to your question, during the current period for the exercise of electors rights, it is the current external auditor that questions should be directed towards.
