How to run a task when variable is undefined in ansible?

Strictly stated you must check all of the following: defined, not empty AND not None.

For "normal" variables it makes a difference if defined and set or not set. See foo and bar in the example below. Both are defined but only foo is set.

On the other side registered variables are set to the result of the running command and vary from module to module. They are mostly json structures. You probably must check the subelement you're interested in. See xyz and xyz.msg in the example below:

cat > test.yml <<EOF
- hosts: 127.0.0.1

  vars:
    foo: ""          # foo is defined and foo == '' and foo != None
    bar:             # bar is defined and bar != '' and bar == None

  tasks:

  - debug:
      msg : ""
    register: xyz    # xyz is defined and xyz != '' and xyz != None
                     # xyz.msg is defined and xyz.msg == '' and xyz.msg != None

  - debug:
      msg: "foo is defined and foo == '' and foo != None"
    when: foo is defined and foo == '' and foo != None

  - debug:
      msg: "bar is defined and bar != '' and bar == None"
    when: bar is defined and bar != '' and bar == None

  - debug:
      msg: "xyz is defined and xyz != '' and xyz != None"
    when: xyz is defined and xyz != '' and xyz != None
  - debug:
      msg: "{{ xyz }}"

  - debug:
      msg: "xyz.msg is defined and xyz.msg == '' and xyz.msg != None"
    when: xyz.msg is defined and xyz.msg == '' and xyz.msg != None
  - debug:
      msg: "{{ xyz.msg }}"
EOF
ansible-playbook -v test.yml

From the ansible docs: If a required variable has not been set, you can skip or fail using Jinja2’s defined test. For example:

tasks:

- shell: echo "I've got '{{ foo }}' and am not afraid to use it!"
  when: foo is defined

- fail: msg="Bailing out. this play requires 'bar'"
  when: bar is not defined

So in your case, when: deployed_revision is not defined should work

As per latest Ansible Version 2.5, to check if a variable is defined and depending upon this if you want to run any task, use undefined keyword.

tasks:
    - shell: echo "I've got '{{ foo }}' and am not afraid to use it!"
      when: foo is defined

    - fail: msg="Bailing out. this play requires 'bar'"
      when: bar is undefined

Ansible Documentation