This is from the dispute settlement chapter of the Modernisation of the Trade part of the EU-Mexico Global Agreement:
Composition of a Panel
1. A panel shall be composed of three panellists.
2. Within [X] days from the date of receipt of the written request for the establishment of a panel by the Party complained against, the Party shall consult with a view to agree on the composition of the panel. For that purpose, each Party shall, within [X] days of the date of receipt of the written request under Article [X] ("Establishment of a Panel") designate a panellist, who may be a national of that Party, and propose to the other Party up to three candidates to serve as chairperson. The Parties shall endeavor to agree on the chairperson from among the chairperson candidates within [X] days of the date of receipt of the written request under Article [X] (Establishment of a Panel). A panelist designated by a Party may be objected by the other Party if it considers that such individual does not comply with the requirements set out in Article [X.7] ("Requirements for Panellists").
3. If the Parties fail to agree on the composition of the Panel with the time period set out in paragraph , the Parties shall apply the procedures set out in the following paragraphs to compose a panel.
4. Each Party shall, within [X] days of the expiry of the time period set out in paragraph 2 appoint a panelist from its sub-list set out in accordance with Article X.6 [X].
5. If the complaining Party fails to appoint its panelist within the period specified in paragraph 4, the dispute settlement proceedings shall lapse at the end of that period.
6. If the responding Party fails to appoint its panellist within the period specified in paragraph 4, the complaining Party may request an appointing authority listed under the Rules of Procedure (Annex) to select the panellist by lot. The appointing authority shall select the panellist from the sub-list of the responding Party established under Article XX, within [X] days of the receipt of the request of the complaining Party,
7. If the disputing Parties fail to agree on the chairperson within the time period established in paragraph 1, the complaining Party, and in case of procedures under XXX [level of suspension] any of the disputing Parties, may request an appointing authority to select by lot the chairperson of the panel from the sub-list of chairpersons established under Article XX, within [X] days from the expiry of that time period. The appointing authority shall select the chairperson within [X] days of the receipt of the request of a disputing Party.
8. For the purpose of paragraphs 6 and 7, the appointing authorities listed in the Rules of Procedures in Annex XX shall serve as an appointing authority for the composition of the panel under this Chapter. The appointing authority shall select the panellist in accordance with the provisions of this Chapter and the Rules of Procedure.
xx. If any of the lists provided for in Article X.6 (Lists of Panellists) have not been adopted by the Joint Committee, the panelists or chairperson shall be appointed from the individuals who have been designated and notified (in writing) to the other Party by a Party or both Parties.
I like what they are trying to do here, although the text does not look like it is completely finished. Note the following disclaimer: "The texts are published for information purposes only and may undergo further modifications including as a result of the process of legal revision. The texts are still under negotiations and not finalised." But if I understand what they are going for, it is simple and clear, unlike many other procedures for appointing panelists.
After posting this, I realized that the rules of procedure are available and identify the "appointing authorities":
III. Appointment of Panellists
7. For the purposes of paragraph 6 and 7 of Article X.5 of Chapter SSDS, the following persons may serve as appointing authority for the composition of the panel:
a) The President of the Appeal Tribunal of the ICS referred to in Article XX of Chapter XX (Investment/ICS); or
b) The Secretary General of the Permanent Court of Arbitration.
I don't know when we'll have an appeal tribunal for ICS, but there should usually be a Secretary General of the Permanent Court of Arbitration in place. What will that person think of making these appointments though?