Math and Logic Puzzles: Redux

[Who]

Spoiler: easy variant

one person turns on the light every time they enter a dark room. everyone else turns off the light if it's on two times and then leaves it alone. once the one who turns on has seen the light go off 199 times, they know everyone has been in the room.

Correct!
Also, although not required by the variant, your new strategy is significantly faster. It takes on average about 20,000 visits, which at one visit per day is around 55 years. They might still be alive by the time they get out.