"be/go out like a light" is a rather fixed expression, so saying "went off like a light" sounds strange.
It's very common to say "the lights go out" when you don't expect the lights to be turned off.
"There was a very big storm last night and all our lights went out." (We lost electricity)
"There was a bolt of lightning and then all the lights in our neighborhood went out." (From houses, street lamps, etc)
"Do you have any light bulbs? This light's out." (This light bulb is dead)
Also common when telling children what time they have to go to bed, is "lights out," as in:
"Alright kids, go brush your teeth. It's lights out at 9 o'clock."
"Go put your toys away, lights out at eight."
(not a teacher, just a language lover)