I, the great electrical engineer, studied the schematic you posted rather carefully, for the screwy arrangement seems very similar to the wiring of my Trac Clipper, which is a Korean Batavus.
I am fairly confident that your diode is not a zener diode, but a plain rectifier diode. That's because a zener diode is almost invariably connected in series with a considerable resistance--generally a resistor--to limit the current through the device when it conducts 'backward.'
It looks to me that the purpose of the diode is to allow the horn to be run off the flywheel magneto's ignition coil. That poor coil has three duties: to supply a large impulse of sharply-cut-off current to the spark coil for the spark, to run the stop light, and to run the horn.
I assume you know the following, but I have to get it straight in my own head. The bike's ignition, or any flywheel magneto, pushes a large current through both the flywheel coil and the primary of the spark coil (actually a transformer) as the strong flywheel magnet approaches the flywheel coil. When the ignition points open, that current is instantly (approximately) stopped, as is the magnetic field produced by that current in the spark coil's primary winding. Since the large secondary coil--the one connected to the spark plug--is also subject to this same suddenly-cut-off magnetic field, the rapid change in magnetism through that secondary coil gives us our 30,000v spark. (Rapid change in amount of magnetism through a coil produces a prodigious voltage across the ends of that coil, or V=d phi / dt.
But our flywheel ignition coil just sits idle for the rest of the time. As the flywheel magnet goes past this coil, it develops a large opposite voltage across its ends, a voltage that could drive current through accessories like the horn.
And so we connect our horn to the flywheel ignition coil. But then if we push the horn button, current from our flywheel ignition coil will happily travel through the horn's internal coil, down through the horn switch, and thence to ground, thus preventing any current from flowing through our spark coil. And the engine will stop.
And so we add a diode, which will only conduct current in one direction, in series with our horn. This will prevent the positive-going current produced when the flywheel magnet is approaching the magneto ignition coil from flowing anywhere but through the spark coil's primary. When the magnet passes by our magneto ignition coil, though, the current changes direction and thus can, when the horn button is pressed, flow through the horn and produce a horrible croaking beep due to the weird current waveform thus produced.
I would guess that you'll want to replace that diode with any silicon rectifier diode capable of conducting, say, 10 amperes of current. The PIV (peak inverse voltage) rating is not so critical, but since we're dealing with ignition voltages here, something greater than 200 volts might be in order.
Don't connect two diodes in parallel in an effort to increase the current rating, for while it's tempting to do so, it doesn't work: one of the diodes always hogs all the current and then burns out for its trouble.
Corrections are invited here, for I've rapidly come to understand that moped wiring is awfully strange. The reason is that they're trying to squeeze all the electric power they can out of that tiny magneto and that tiny engine.
if the parts ever come I'll try building a half-wave voltage doubler to increase the lighting coil's output to 12v DC and thus maybe run some LED lights.