I had fun wasting hours working out how to do correct ‘when’ statements in Ansible - In end up consulting #ansible on IRC to get the answers.
Anyway I hope the following playbook makes sense to you. Note that ‘admintool’ is a valid group in my situation.

- name: Debug all the things
  hosts: all

  tasks:
    - set_fact: renew_cert="renew"

      # Valid - Should pause
    - name: Test 0 PASS
      pause: prompt="Test" seconds=1
      when: '"admintool" in group_names and renew_cert == "renew"'

      # Valid - Should skip
    - name: Test 1 SKIP
      pause: prompt="Test" seconds=1
      when: '"I-Dont-Exist" in group_names and renew_cert == "renew"'

      # Valid - Should skip
    - name: Test 2 SKIP
      pause: prompt="Test" seconds=1
      when: 
        - "'i-dont-exist' in group_names"
        - renew_cert == "renew"

      # Valid - Should pause
    - name: Test 3 PASS
      pause: prompt="Test" seconds=1
      when: 
        - "'admintool' in group_names"
        - renew_cert == "renew"

      # Invalid - Should skip - but eval's True - DONT USE
    - name: Test 4 SKIP
      pause: prompt="Test" seconds=1
      when: ("'admintool' in group_names" and renew_cert == "renew")

      # Invalid - Should skip - but eval's True - DONT USE
    - name: Test 5 SKIP
      pause: prompt="Test" seconds=1
      when: ("'I-dont-exist' in group_names")

      # Valid - Should pause
    - name: Test 6 PASS
      pause: prompt="Test" seconds=1
      when: ("admintool" in group_names and renew_cert == "renew")

      # Valid - Should skip
    - name: Test 7 SKIP
      pause: prompt="Test" seconds=1
      when: ("I-dont-exist" in group_names and renew_cert == "renew")