Pablo, thanks for the reply. 

I have 

<field name="body_html" widget="html" options="{'style-inline': true}"/> 

for the email template editing View (when I inspect in development mode and go to edit form: view), however, there is still no option on the WYSIWYG inline toolbar to display source/code in the editor.

I've found out that I can force it to display raw text in there by changing to widget="text" but that's not an ideal solution since I have to open the XML and manually switch back and forth.

Is there something else I'm missing that can get the source code view option back on the toolbar of the editing widget?

I have tried this in Odoo 14, so I'm not sure whether it will work in version 13, but you can insert the html of the code view button somewhere in the toolbar and the button will be working as expected: <button type="button" class="btn btn-secondary btn-sm" title="" data-event="codeview" tabindex="-1" data-name="codeview" data-original-title="Code View"><i class="fa fa-code"></i></button>

An easier solution is to directly edit the page html, modify the mail body and Odoo will accept the change.

Try with debug mode activated. You will then see Codeview

The options="{'style-inline':'true'}" is the solution to the question!! Just adding the widget is not enough.

The Ckeditor configuration option style-inline has to be set to true... Until today i was used to configure ckeditor settings via an ckeditor.js file, but in the odoo context i am not able to identifiy how to overwrite an existing config file or add an own file via a custom addon.. If anyone knows how to implement an own ckeditor.js config file, please let us know =)