I use the W3 Total Cache WordPress Plugin for the majority of cache related performance optimisation and have the plugin set to add the relevant Last-Modified Headers and ETag Headers rules to the sites .htaccess file.
You can see in the screenshot above both options are ticked:
Set Last-Modified header (ticked)
Set the Last-Modified header to enable 304 Not Modified response.Set entity tag (ETag) (Ticked)
Set the ETag header to encourage browser caching of files.
The above options should result in the favicon.ico file being cached correctly.
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