The lantern was a toy that varied quite a bit from its instruction sheet. There are only three lengths of dowels to choose from with this set. The dowel holding the lantern in the drawing is somewhere between the long and the medium-length dowels.
I experimented with both lengths. The long dowel gave the best results. Also, note that there's no light shining through the lantern. That's strictly artistic license. In the 21st Century, it's possible to thread a small LED light into the box (although you couldn't hide the wire. But in the 1930s when this toy was sold, you'd have to just rely on your imagination.