A vacancy in a trusteeship occurs if: A person designated as trustee rejects the trusteeship; A person designated as trustee cannot be identified or does not exist; A trustee resigns; A trustee is disqualified or removed; A trustee dies; A guardian of the person or guardian of the property is appointed for an individual serving as trustee; A trustee cannot be located for 120 consecutive days; or A trustee is unable to handle business affairs as determined by two licensed physicians. If one or more cotrustees remain in office, a vacancy in a trusteeship need not be filled. A vacancy in a trusteeship shall be filled if the trust has no remaining trustee. A vacancy in a trusteeship that is required to be filled shall be filled in the following order of priority by a person: Designated in accordance with the terms of the trust to act as successor trustee; Appointed by unanimous agreement of the qualified beneficiaries; or Appointed by the court. The court may appoint an additional trustee or special fiduciary whenever the court considers the appointment necessary for the administration of the trust, whether or not a vacancy in a trusteeship exists or is required to be filled.