i like the fact that the speedometer is also a rev counter, which is neat, but doesn't really make sense with only one needle and three speeds.
i guess it is calibrated to read revs in 2nd gear, ie at 1:1.
nonetheless, if you can get it to work, it'll be an absolute must to keep it there. any idea how rare something like that must be (I don't either, but I'm guessing the answer is something like VERY)?
speedo problems: usually in this vintage it's a spring cable driven by a swaged or welded gear at one end (in the gearbox i would guess in this setup, but can be the hub centre). the cable is flexible but rigid enough to be driven without too much wind-up. the end (behind the speedometer) terminates in a section where the spring has been compressed from a tube into a square or triangular profile, and this inch or so of shaped wire fits into a socket in the back of the speedo by a screwed on collar. as the wire turns, it turns the indicator against soem kind of spring resistance: the faster the cable turns, the more the lever you see from the front moves.
if the speedo doesn't work, usually it's 1) the cable has broken or frozen in its hosing. 2) the cable has dropped out of the socket behind the speedo unit on the bars, or 3) the gear on the end at the hub/gearbox has either dropped off, is out of alignment, or has had its little teeth worn off by corrosion or grinding. 3 can happen if 1 happens first. if 3 has happened, you're usually SOOL unless you can weld or machine a new one one.
checking and fixing: detach the cable from the rear of the speedo unit by unscrewing the collar. use pliers (wrapped in cloth to avoid stripping the collar grooves). lube first with WD40 or similar to allow easier unscrewing.
insert a small wooden stick or rod or even a screwdriver that will fit into the rear socket, and spin. bboth ways! to see iffthe needle turns. if it does, you're in luck.
twist the cable and see if it spins freely: frozen cables won't budge, broken gears at the other end will allow you to spin too easily, and loose gears at the other end turn with a ratchet.. don't overdo the spn test.
pick up the rear of the bike, and look at the cable as you spin the back wheel (if it's hub mounted) or the cranks (if it's gear box mounted): does the cable turn? if it does, then you're also in luck and the gear at the end of the cable will probably be OK.
wash the cable by filling the housing well with light oil and spinning the hell out of it for a while. (best if disassembled, but not totally necesary) then drain by gravity and replace oil, drain again and finally lube the cable in its housing well with a heavy oil or a specialist cable lube used in brake and gear cables in those motorsickel things. try not to disassemble the speedo unit if you can, they're a finicky fix at best and usually need a few sacrifices to get good at (ie, don't try to overhaul the best one first, but practice on one from your dad's car first til you get it right.)