Good question. Yes, I've tried
include("file.php");
In fact, I've tried it every which way. The above code (yours) works fine under normal http. It does NOT work from behind the https. I've found that with image tags, I have to use a full URL from behind https. So I tried a full URL for my include. That doesn't work either. Whether I use full URL or relative, it tells me it can't find the file to include, and that the include_path = ".:" etc etc.
I think the answer lies in some of the PHP settings but I just need more guidance in getting it working.