(1) A vacancy in a trusteeship occurs if 1 or more of the following occur:
  (a) A person designated as trustee rejects the trusteeship.
  (b) A person designated as trustee cannot be identified or does not exist.
  (c) A trustee resigns.
  (d) A trustee is disqualified or removed.
  (e) A trustee dies.
  (f) A guardian or conservator is appointed for an individual serving as trustee.
  (2) If 1 or more cotrustees remain in office, a vacancy in a trusteeship need not be filled. Though any separate trustee may comprise a cotrusteeship, the relation between respective separate trustees serving under a given separate trustees provision is not itself a cotrusteeship. A vacancy in a trusteeship must be filled if the vacancy leaves either of the following:
  (a) A trust that is not subject to a separate trustees provision as of the time of the vacancy without any remaining trustee.
  (b) Any of the several separate trusteeships governed by an operative separate trustees provision without any remaining trustee.
  (3) If a vacancy in a trusteeship of a noncharitable trust is to be filled, the vacancy must be filled in the following order of priority:
  (a) In the manner designated by the terms of the trust.
  (b) By a person appointed by the court.
  (4) If a vacancy in a trusteeship of a charitable trust is to be filled, the vacancy must be filled in the following order of priority:
  (a) In the manner designated by the terms of the trust.
  (b) By a person selected by the charitable organizations expressly designated to receive distributions under the terms of the trust if the attorney general concurs in the selection.
  (c) By a person appointed by the court.
  (5) Whether or not a vacancy in a trusteeship exists or is required to be filled, the court may appoint an additional trustee or special fiduciary upon the showing of good cause.
  (6) As used in this section, “cotrusteeship”, “separate trustee”, “separate trustees provision”, and “separate trusteeship” mean those terms as defined in section 7703b.