Manually Set Location Services Location My iMac rarely has WiFi turned on since I use Ethernet, however Location Services seem to need a WiFi connection (they both connect to the same router, so I fail to see the logic there… but there we go).

Is there a way to override or set my location so that apps which use Location Services can still get a location?
It seems that you can need wifi on (but not necessarily configured) in order to get location, Core Location works using skyhook and will not function without wifi on. This is not well documented by Apple but this StackOverflow conversation covers it. 

According to the above, you should be able to turn on Wifi, wait for a location fix and then turn it off. 
If that doesn't work look into WhereAmI, this project allows command line access to CoreLocation and you should be able to script it and wifi to turn on once in a while, log your location and then turn wifi off.