I would double check the flex cable connection from the display assembly to the logic board. Take a look at the pins on the flex, and the pins on the FPC connector (where it connects on the logic board). Make sure they are both clean and free of debris.
Once that is verified, I would attempt an SMC/PRAM reset on the device.
- With the machine off, plug in your charger
- Hold down Shift+Control+Option+Power
- Release key combination after 10 seconds
- Turn the device on
- Hold down Command+Option+P+R
- Keep holding, wait for the second startup chime and then release
- Allow the device to boot into macOS
- Check your FaceTime camera again