If the conservatee wishes to petition the court for termination of the conservatorship or for removal of the existing conservator or for the making, modification, or revocation of a court order under Chapter 4 (commencing with Section 1870) or for restoration of the right to register to vote, or if, based on information contained in the court investigator’s report or obtained from any other source, the court determines that a trial or hearing for termination of the conservatorship or removal of the existing conservator is in the best interests of the conservatee, the court shall notify the attorney of record for the conservatee, if any, or shall appoint the public defender or private counsel under Section 1471, to file the petition and represent the conservatee at the trial or hearing and, if such appointment is made, Section 1472 applies.