When creating new site templates in SharePoint 2013, ensure you check the box to include content. If you don’t do this, any sites created from your new template will have the “Change the look” functionality missing, it will load a blank page as shown below:
To resolve this, include the content when saving the new site template. Ensure that there is no test data on the lists / libraries etc.
Include content enabled:
After creating a site from this new template, the “Change the look” functionality will work as expected: