(a)    Appointment by Agreement. Within 10 days of the court order of referral, the parties may file a stipulation with the court designating a mediator certified as an appellate mediator pursuant to rule 10.100(f), Florida Rules for Certified and Court-Appointed Mediators. Unless otherwise agreed to by the parties, the mediator shall be licensed to practice law in any United States jurisdiction.

(b)    Appointment by Court. If the parties cannot agree upon a mediator within 10 days of the order of referral, the appellant shall notify the court immediately and the court shall appoint a certified appellate mediator selected by such procedure as is designated by administrative order. The court shall appoint a certified appellate mediator who is licensed to practice law in any United States jurisdiction, unless otherwise requested upon agreement of the parties.

(c)    Disqualification of Mediator. Any party may move to enter an order disqualifying a mediator for good cause. Such a motion to disqualify shall be filed within a reasonable time, not to exceed 10 days after discovery of the facts constituting the grounds for the motion, and shall be promptly presented to the court for an immediate ruling. If the court rules that a mediator is disqualified from a case, an order shall be entered setting forth the name of a qualified replacement. The time for mediation shall be tolled during any periods in which a motion to disqualify is pending.

(d)    Substitute Mediator. If a mediator agreed upon by the parties or appointed by the court cannot serve, a substitute mediator may be agreed upon or appointed in the same manner as the original mediator.

(e)    Compensation of a Court-Selected Mediator. If the court selects the mediator pursuant to subdivision (b), the mediator shall be compensated at the hourly rate set by the court in the referral order or applicable administrative order. Unless otherwise agreed, the compensation of the mediator should be prorated among the named parties.