Server-side includes on an iMac I have failed for a year to find a way to run SSI (server side includes) on my iMac using the apache web server included with server.app.

I am wondering if the server app will allow server-side includes in a website hosted by Apache on High Sierra?
No. In fact, Apple is removing the web server functionality from server app entirely in the very near future and documenting how you would migrate your data to apache to serve web pages. 


http://krypted.com/mac-os-x-server/apple-releases-service-migration-guide-macos-server/
https://developer.apple.com/support/macos-server/macOS-Server-Service-Migration-Guide.pdf


The PDF above has pages 22 to 32 dedicated to how you would migrate any data to an open-source web server. If you like apache, the homebrew tool might be a good one to use for managing that install and patching and service state (stop / start / restart the web server on command or boot).

From there, you'd be on your own (or need to ask a flown question - possibly on another site about how to enable the SSI you want on the version of the web server you have chosen).