Green light glowing on back of Apple Watch
How can I turn off the constant green light on my Apple Watch?
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Those are the heart rate sensors. See the 'How Apple Watch measures your heart rate' section in:
Monitor your heart rate with Apple Watch - Apple Support
They should not be constantly staying on or it will drain your battery very quickly.
The first (and simplest) thing to try if something isn’t working right is to restart your Apple Watch and its paired iPhone. If necessary (device not responding), try a forced restart. Both methods can be found here:
How to restart your Apple Watch - Apple Support
Restart your iPhone - Apple Support
If that doesn't help, the next steps would be to unpair and pair your watch again and restore from the backup just created. This should result in no loss of data. It deletes all temp and corrupted files and re-indexes the file system.
Unpair and erase your Apple Watch - Apple Support
Set up your Apple Watch - Apple Support