That is a REVCO Reverse aftermarket kit. The outer mechanism is attached to a large aluminum screw that takes place of the original stitch length knob. Then the lever is connected to the inner parts of a the machine via linkage around the front and under the hand wheel.
The Reverser doesn't actually sew in reverse, what it does is make the machine capable of back tacking.
At least that's the way the one I have works.
One of our other members has a link to the original patent drawings for this unit. It's quite interesting. Perhaps he'll see this thread and post the link again.
Joe