What a coincidence!
That's funny - just last night I was wandering aimlessly around the shop, and I came across a similar unit made by a company called Jones Motrola. (No, not "Motorola") It's probably very similar inside, but it's got a bit more corrosion.
Mine has a cover that comes off of the back, and the "speed change" knob is on the front. Looking at the gears you have there, you see the two parallel bars running vertically from the top to the bottom of the gear cage? On my unit, the speed change knob has a pin that rides between those vertical bars. It turns the entire gear cage about +/- 20 degrees or so. The middle position on mine gives the 1:1 ratio, deflecting the cage to one side engages the "gear up" function for low speed, and deflecting the other way gears it down for the high speed range. When the gearbox is in the "middle" position, the large gears move closer to each other and the "V" parts engage. When the gearbox is deflected left or right, the big gears move away from each other and one of the gear pairs on the sides will engage to increase or decrease the speed ratio.
The meter movement on mine comes off separately, and I was able to clean it up so it works. I've got to dig up a really small allen wrench so I can take more of it apart for cleaning.
Oh, and in case you might have wondered. The buttons that protrude from the sides control a slider that allows the reading to be held on the meter when the tach is disengaged from the rotating part.
Hmmm. Maybe I'll try to post some pics. I'll need to take some other pics down to do it.
Science. If you don't understand it, don't talk to me about how it's going to end the world.