[Verizon Samsung Galaxy S III] joshindc:
So, I haven't tested it for this (although I am now...) because I just have the charging LED setting turned off. I think this should work fine, although if you've killed the battery full notification you might get the green light coming on once charging completes (which you can probably deal with with an additional profile). Here's a more detailed description of the task setup:

1) Open Tasker and go to the 'Tasks' tab at the top of the screen.

2) Click on the green [+] at the bottom of the page to create a new task. Then name it something (LED kill?) and tap the green check button.

3) Click the [+] in the lower right hand corner to add an Action to your task.

4) Select 'Script', then 'Run Shell' from the Menus that pop up.

5) Under 'Command' type "echo 0 > /sys/devices/virtual/sec/led/led_pattern" without the quotes

6) Check the 'Use Root' box, then click the green check at the bottom of the window.

7) Now you should see the Task Edit window. Click the blue 'play' button at the bottom right of the window to run the task now. If you get a Superuser popup make sure you've checked the box to remember your selection, and accept the SU request. Now tap the green check box to save the task.

* Now you have a task that can turn off the light, but you need a way to trigger it. In tasker you do this by setting up profiles, which you can think of as triggers that will call the task. We want to trigger it to kill the LED whenever the phone turns it on. The phone will turn on or change the light at 2 different times:

A) When you receive a notification

B) When you turn off the screen (This will 'reset' the led if you turn on the screen and then turn it back off without clearing the notification) It will also turn on the led if the phone is charging and you've left that setting checked.

So, lets proceed:

8) Tap the 'Profiles' Tab at the top of the screen.

9) Tap the green [+] to create a new profile. Name it something like "Notification Kill" and click the green check box.

10) Select 'Event', then 'UI', then 'Notification' from the menus that pop up. Click the green check at the bottom of the Notification window that pops up (all the default settings are fine).

10a) At this point I think I was prompted the first time I did this to add Tasker to the accessibility permissions. If this happens, scroll down in the accessibility settings window that pops up and check the box next to Tasker. Then hit the back button to go back to Tasker.

11) Now select the task you just created (LED Kill) from the Task Selection window that pops up

* Now if you leave Tasker you should be blocking all notification LED lights. But you only want to turn them off at night! So you need to add another Context to this profile.

12) Long press on the Context (left hand side of the profile you just created where it says 'Notification *,*' and has a Orange ! triangle)

13) Select 'Add' from the popup, then select 'Time'

14) Pick the time range that you want the LED turned *OFF*. In your case you should pick From: 23:00 and To: 07:00.

15) Click the green Check and you're done with this profile.

* Now you've taken care of the (A) reason for the light coming on. But you need to take care of (B) as well, in case you check your phone during the 'night' hours, or if it's plugged in.

16) Repeat step (9), but name it 'ScreenOffLEDKill' or something easier to type.

17) Select 'State', then 'Display', then 'Display State' from the popup menus.

18) Make sure 'Off' is selected from the 'Is' dropdown menu, and click the green check box.

19) Select the task you created earlier again (LED Kill)

20) Repeat Steps 12-15 for this profile (Long press on 'Display State Off'...)

Now you should be set! If this still isn't working let me know and I'll try and troubleshoot it with you.