Find my iMac - a question please

You need to enable Location Services in the iCloud control Panel under Find My Mac Details...

macOS Sierra: Use Find My Mac

If you mac has no wi-fi chip it wont allow you to use location services

if your mac has a wi-fi chip but is only connected to the wired connection your location services will not work

if your mac is connected to wi-fi and ethernet regardless of connection order (wi-fi primary, cable second or wi-fi secondary, cable primary, or any other combination) you can use find my mac.

If your device is stolen their is no assurance it would even be plugged into any network, but in the event it is you may have some way of getting it, just as there is no assurance if your car has an anti theft device and is stolen that the car anti-theft device will be take out and annihilated in a trash compactor, or the car will be cut into parts and delivered all over the world. Everything has a limitation or a workaround when it comes to anti-theft.

you can remote lock over wired connection but location will not be available unless you are using Wi-Fi, you will get this with location services on, but wi-fi off:

and if you are on a mac that does not have any wi-fi you will get this warning:

I'm marking my own as helpful because I did not know this myself until just a few minutes ago.

Way to go me! I earned that 2nd cup of espresso today!

Disconnect from Ethernet. Wait a few minutes, then check to see if it appears in FMiP.

Why are you connected to both WiFi and Ethernet? That can seriously mess with things. Location services being one of those.

Nope, you can do it. I have a dozen systems on both, wi-fi as primary so it does not take down our internal network when we send and receive dozens of GB's of data all day long, then use ethernet for local servers. It has seriously increased productivity because what took hours takes minutes and it does it for a fraction of the cost.

and with wi-fi on and ethernet on it found my Mac on iCloud instantly.

In the case of the OP, I'd really like to know why they're connected to both... for all we know, the WiFi network they are connected to is internal only and has no connection to the Internet at all. I've seen that before.

Maybe, I've run into some problems where the Wi-Fi gateway goes snafu and everyone defaults back to the wired network and tries to stuff 100lbs of manure into a 5lb. bag - our wired network here is so old it may be token ring - but when this happens with everything on the Wi-Fi range, PC's, Androids and whatever else is connected, but thats as much as I've seen.

Oh, I'm not saying it can't be done... just that it can cause some issues. Usually local to the machine rather than to the network.

The conclusion is if someone comes in my house to rob my family the police can take their time, I'll handle it myself. The rest of it I've already explained fully.