This app was mentioned in 4 comments, with an average of 1.75 upvotes
You may probably be the first one to know, but I'm working on an update to my app LED Control to add notification support. I hope I can get it to work on the new Moto G as well.
There is a specific setting for the light being on while the screen is on, not sure if there is one for it being off though.
Not sure why it wouldn't work for you. Maybe try this app if you're rooted.
You ever figure this out? I use this which does the job just fine if you have root, although it doesn't always persist through a reboot.
https://play.google.com/store/apps/details?id=com.kdb.ledcontrolfree