We ran an evaluation about this issue some years ago and changed the SOP/ FOM after 3 months testing during sim training.
PNF/PF announces non-normal condition
PF orders: non-normal checklist (title of NNC) my controlls, my radio
PNF deals with checklist
When checks completed PNF confirms: End of checklist, my radio
This allows the captain also to decide about PF after malfunction is announced.
Worked charming. EU airline.