When Coop is in the mauve room/white lodge with Naido and she takes him up the ladder on the roof, she is desperately trying to explain something to him. Coop is frustrated and can't understand the way she communicates. I wonder if her next action is simply to show him how things work...
She next goes to the 'bell shaped' thing that we've seen in The Fireman's place and she pulls the
switch (electrical I assume) and holds the bell to initiate what seems to be a deadly electrical shock. Then she falls, endlessly into the void.
THEN we see Major Briggs saying "Blue Rose"
THEN when Coop goes back in the room, American Girl's watch changes to 2:53
Major Briggs left the note for Truman/Bobby/Hawk/Andy to be at that location at 2:53, he knew Naido would be there at that time, having fallen/shocked herself into the other world.
Naido was showing Coop how to travel with electricity. He didn't understand then. But he remembers this when he uses the fork in the socket after hearing Gordon's name.
Maybe someone else has put these pieces together, but thought I'd post it if not...we have yet to see what other significance Naido has in the story, but it sure seems like "she's important"!