LED on Xperia Z only in operation while charging
This is a known bug in Xperia Z (sources 1 and 2).

Currently the only way to restore the LED functionality is to:


de-select Settings -&gt; Backup &amp; reset -&gt; Backup my data and Automatic restore
perform a factory reset from Settings -&gt; Backup &amp; reset -&gt; Factory data reset
Complete the reset manually (that is, without restoring apps/data from the Google account)


Hopefully this will be corrected in the next update.