It is possible to simply add Enterprise Admin Action Logging for a custom module adding a logging.xml and declare a group and afterwards enable this group in the configuration.
Stores > Settings > Configuration > Advanced > Admin > Admin Action Logs > Your Group Name
If you add a new one it will be disabled by default
Take a look at the following code sample:
etc/logging.xml
<?xml version="1.0"?>
<!--
/**
* Copyright © 2016 Magento. All rights reserved.
* See COPYING.txt for license details.
*/
-->
<logging xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Logging:etc/logging.xsd">
<groups>
<group name="group_identifier_here">
<label translate="true">Action Group Label here</label>
<expected_models>
<expected_model class="Vendor\Module\Model\Class" />
</expected_models>
<events>
<event controller_action="fullcontroller_actionname_here_save" action_alias="save" />
<event controller_action="fullcontroller_actionname_here_delete"
action_alias="delete" />
</events>
</group>
</groups>
</logging>
