The plate for this one is on top of the coffin in niche 11, but that's not where it goes.
The sketch and the clue to the right coffin can be found in the ruins --
-- after you watch the film reel you find there.
Where can I play this movie reel?
The riddle says, "Two handles pull out the box" -- okay, so it has two handles rather than one.
It then says, "From the middle it shints, rising above them all." So it's in one of the middle columns and on the top row. That makes it niche 2.
Here's how I solved the tangram:
Inside is an odd little brooch that's going to turn out to be very important when you get to the endgame.