Hey, man; thanks for having taken the time to work that out on paper for me. I think I understand the concept, or at least I thought I did. In the gizmo I'm building, there are 2 identical gears each engaged with the other. The output gear turns clockwise which means the driven gear turns counterclockwise. The driven gear is fixed to the large pulley, and via a belt, turns the small pulley. As desired, both pulleys turn counterclockwise.
In your drawing, there is a point that confuses me. Your output gear rotates counterclockwise. As drawn, it is engaged with pulley A which turns clockwise. I'm with you to this point. Then pulley A the driven gear is engaged with pulley B, the idler gear, which appears in your drawing to also be turning clockwise...and visa versa when the lever is toggled, and the idler gear engages directly with the output gear. I guess what I'm unclear about is that before the toggle, both A & B are turning clockwise, and after the toggle, both A & B are still turning clockwise.
That said, I think I found enough in the way of gears, and shafts to attempt to make something work. I'll stick close by so you can help me understand better what confuses me now.