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

Step 1: Enable Email-to-Case

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

Step 2: Enable Case Feed Actions and Feed Items

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

Step 3: Enable Feed Tracking for Cases

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

Step 4: Verify Email Deliverability Settings

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