Your comments

I think it was step 9 I missed initially. You need to have an incoming screenconnect session to add the privacy setting properly.  This will be a nightmare if you have to do this after every update though as a lot of my Macs are headless.

I've just tried deleting and adding again from the privacy screen and on the second attempt, it worked... very strange...

It seems to work OK on machines that haven't had SC on them before, but the ones I have tried with existing SC connections even after ending and reinstalling do not appear to work properly...

I can connect and see the screen, but cannot control using the keyboard or mouse.  I'll contact support.

Any updates on this issue please? The above fix didn't work for me, but I was able to get a VNC program to run by adding VNCAgent in the privacy box.  I have a few headless Mac servers I am wanting to upgrade to Mojave, but cannot do that until this is resolved.

The dummy HDMI emulators solved the problem

I've just ordered a dummy HDMI emulator for Amazon to try... I'll update the thread next week...

I'm at one of the clients today and plugged a HDMI cable in.  Here's screenshots showing the difference:

With HDMI cable plugged in

No HDMI cable plugged in

As you can see the top menu is missing and the desktop icons are missing...

They're on 10.13.4. The ones which work are also on 10.13.4. The only difference is lack of keyboard, monitor & mouse as far as I can tell.

Yes, I have two headless and 4 with keyboards, mice & monitors attached. Only the 2 headless are affected.

I have the latest Java (v8 171), but I've also tried connecting from multiple machines with the same result. It's an Access session.