The oath required by this chapter shall be taken and subscribed by:
(a) Every person who is appointed to a State position not in the State civil service and not otherwise so required by law, within 30 days of the date of appointment; and
(b) Every person who has not previously taken and subscribed the oath and who is employed in a permanent position in the State civil service where the employment continues for 30 days or more, within the first 30 days of his employment.