Email publisher action is not visible on Case after it is added to the page layout

The inability to locate the  Email Publisher action to add on a Case page layout may be because "Email to Case" is not enabled for the organization. To Enable:

In Classic:  Setup | Customize | Cases | Email to Case | Edit | Check 'Enable Email-to-Case' | Save
In Lightning:  Setup | Feature settings | Service | Email-to-Case | Edit | Check 'Enable Email-to-Case' | Save

Further Considerations

1.  Ensure "Enable Case Feed Actions and Feed Items" is enabled under support settings. To modify Support settings 

• In Classic: Setup | Customize | Cases | Support Settings.
• In Lightning: Setup | Feature Settings | Service | Support Settings

Please review article about changes that will take place by enabling the above setting: https://help.salesforce.com/htviewhelpdoc?err=1&id=case_interaction_upgrading_cases.htm&siteLang=en_US

2. If the setting "Enable Case Feed Actions and Feed Items" is not found under support settings, make sure "Feed Tracking" is enabled for case object.  To enable Feed Tracking:

• In Classic: Setup | Customize | Chatter | Feed Tracking | Select Case object | Enable Feed Tracking | Save
• In Lightning:  Setup | Feature settings | Chatter | Feed Tracking | Select Case Object | Enable Feed Tracking | Save

3. The email Deliverability settings | Access level must be set to 'All Email' or this component will not render.
 

• In Classic: Setup | Email Administration | Deliverability | Set Access Level to 'All Email' | Save
• In Lightning:  Setup | Email | Deliverability | Set Access Level to 'All Email' | Save