The Red Gem is found in the level N. Sanity Peak. Progress through the level until you reach the chamber with the mask Lani-Loli. You need to jump on the platforms in the correct order to make the Red Gem appear. There is a drawing of the route you need to take on the wall just before you enter the chamber. Starting with the bottom left platform, move around the room counter-clockwise from platform to platform until you've jumped on all of the outer platforms, then jump onto the center one. The gem will then appear just in front of Lani-Loli.