Detecting when Avatar is turned off?

What event do I use to detect it?

Not easily thats for sure.
You could start a timer with the duration of avatar when avatar is pulled off then when the timer expires well then you do your magic.

Now if you only needed to check if avatar was off then its easy just check if the unit has the buff.

Maybe there's something under "Unit - Specific Unit Event"?

Just do a check unit buff every .01 seconds

If buff off then do......

That should work, you might miss something by .009 seconds but I think you can live.