FaceTime HD camera stops transmitting live video in Catalina -- how to fix?
I know this is an old question, but just in case it helps someone else who lands on this page: it seems this is related to a bug with MacBook Pros after they wake up from sleep. You can deal with it by simply restarting the camera plugin. Close the videoconference app, open Terminal and type:
sudo killall VDCAssistant

Type in your password at the prompt and that's it. If the issue was related to the wake-up-from-sleep bug, then the Thunderbolt Display camera should be working once you start the videoconference app again.