hmm quite hard to check if the Ethernet connection is recognized at all without screen attached.
What you could try to trigger a reboot, is to have a look into the tool ifplugd. We played a little bit in the past to switch Ethernet to WiFi once Ethernet got detached. But it should work in your case as well. Once the network cable removal is detected, a reboot could be triggered. It’s just a matter how you define the ifplugd.action
https://dietpi.com/forum/t/using-ethernet-wlan-interfaces-not-at-the-same-time-in-v6-30/4251/1