tell-tale file to know whether Mojave is installed I'd like to revert to High Sierra from Mojave via Time Machine.  I've already wiped the drive and installed a Mojave Time Machine backup, but I'd like to go back even further.  The presence of what directory or file in the Time Machine history will be indicative of whether Mojave or High Sierra is installed?

Thanks
From what the question seems to imply:

the most significant file that the macOS system writes for itself is perhaps its own version number file?

That file is located at 

/System/Library/CoreServices/SystemVersion.plist


If that file contains, for example:

&lt;?xml version="1.0" encoding="UTF-8"?&gt;
&lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt;
&lt;plist version="1.0"&gt;
&lt;dict&gt;
        &lt;key&gt;ProductBuildVersion&lt;/key&gt;
        &lt;string&gt;16G1618&lt;/string&gt;
        &lt;key&gt;ProductCopyright&lt;/key&gt;
        &lt;string&gt;1983-2018 Apple Inc.&lt;/string&gt;
        &lt;key&gt;ProductName&lt;/key&gt;
        &lt;string&gt;Mac OS X&lt;/string&gt;
        &lt;key&gt;ProductUserVisibleVersion&lt;/key&gt;
        &lt;string&gt;10.12.6&lt;/string&gt;
        &lt;key&gt;ProductVersion&lt;/key&gt;
        &lt;string&gt;10.12.6&lt;/string&gt;
&lt;/dict&gt;
&lt;/plist&gt;


Then the above is for Sierra 10.12.6.