There seems to be a couple of misunderstandings here.
BB has not just become deputy mayor, he has been for a long time. Indeed I think he is not councillor/deputy mayor for the district but is also elected at the next level up.
However, EPO staff are allowed to take up representative positions (whether this applies to contracted and senior staff I do not know) but in my day if elected a staff member could ask for (unpaid?) leave to perform elected duties.