I want the majority of my posts to display in full on my home page so I have the “Display post excerpts” check box unchecked. However, I also want some longer posts to only show an excerpt. For those posts I add I add the more code to the post <!–more–>. But for some reason the read more link isn’t showing up on the website.
You can see on my main page at www.artifacting.com that the post titled Pretty/Dirty is an excerpt but it doesn’t show the read more link
I used the shared child theme on my test site and the read more button is displaying for me for the posts having <!–more–> so it seems you have either not shared the updated child theme from your site or you are changing it using custom CSS or using any another plugin.
I don’t see any code in your shared CSS code that is causing it.
Please try deleting the Sparkling theme on your site and installing fresh latest version of it.
This can be due to plugin conflict on your site so please try temporary deactivating all plugins and see whether everything works fine and then enable the plugins one by one to see which plugin is conflicting if any.