omit_placeholder.yml

- hosts: localhost
  tasks:
    - include: task1.yml
    - include: task1.yml arg={{ blah|default(omit) }}

output.txt

$ ansible-playbook omit_placeholder.yml -l localhost

PLAY [localhost] *****************************************************************************************************************************************************************************

TASK [Gathering Facts] ***********************************************************************************************************************************************************************
ok: [localhost]

TASK [debug] *********************************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": "task1 included"
}

TASK [debug] *********************************************************************************************************************************************************************************
skipping: [localhost]

TASK [debug] *********************************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": "task1 included"
}

TASK [debug] *********************************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": "task2 included arg=__omit_place_holder__7623bf129fadd0e0233ebe365031ad078f31facd"
}

PLAY RECAP ***********************************************************************************************************************************************************************************
localhost                  : ok=4    changed=0    unreachable=0    failed=0   

task1.yml

- debug: msg="task1 included"

- include: task2.yml
  when: arg is defined

task2.yml

- debug: msg="task2 included arg={{arg}}"