What are the requirements for someone to train CAP members in their ground team member level 3 tasks? Do they just have to be GTM3 qualified and have their SQTR completed?
They need to be a qualified evaluator in accordance with CAPR 60-3, paragraph 2-2 to sign off on tasks. That does not prevent other members from supervising them on missions or providing other instruction, but the tasks need to be signed off by a qualified evaluator. For ground team members that would be a member qualified to the same level or higher or other specialties that can sign off. For example a Ground Branch director could sign off on tasks done remotely if they can verify accomplishment, but they don't have to. See CAPR 60-3.
Additionally, some wings have chosen to limit their list of evaluators further via approved supplement, so you may want to check with your wing to be sure that has not been done.