Some people are reporting problems with their LED notification on the Sony Xperia Z. It seems that the notification light only lights up when charging according to reports. At first, it was thought the problem might be related to the Stamina mode being enabled. However, even with this switched off people were still not receiving notification of missed calls and SMS texts.
Luckily, there appears to be an easy fix for this. All you need to do is to factory reset the handset. Then apply all of your settings manually such as Wi-Fi i.e. don’t use backup to restore your settings. Many are reporting that once you do this the notification light works as intended. Hopefully, this bug, will be sorted out in the next firmware update.