So, what is the common link between the two cylinders?
Not much is common to both cylinders. I'm not at all familiar with the Laverda 750 twins, but I presume the ignition circuits for each side are pretty much independent of one another. The only common parts would be the 12V feed from the ignition switch, up to the point where it divides to feed each coil. Then perhaps the coil mountings if they are on the same bracket, and that's only relevant if they're the type of coil that needs to be earthed to the frame.
Of course, you could have one or more faults on each of the two ignition circuits, and they don't necessarily have to be the same. For example, you might have a dud condenser on one side and a dud spark plug on the other.
You just need to go through the system logically and check each component. You'll need a multi meter.
1. Check that you have 12V at each coil when the ignition is on and the kill switch is in the "run" position.
2. Check the coils with your meter. Disconnect the wires to them and measure resistances with your meter. The resistance between the two primary connector pins should be around 3-5 Ohms. Resistance through the secondary circuit will be around 6,000 to 10,000 Ohms. Bear in mind all the previous discussion about earthing them or not, depending on the type of coils you're using. If you have ballast (series) resistors in the coil circuit, you'll need to check them too. They'll be around 1-5 Ohms.
3. Check that the points are functional. You can do that with your multi meter on a volts scale. First switch the ignition on. If the coils are OK there should be 12V across the points when they're open and zero when they're closed. You can also use a 12V globe as an indicator. When connected across the points, the globe will light when the points open and go off when they're closed. This can be a handy device when setting the timing.
4. Check the condensers. There is a process to do that with a multi meter, but it's not for beginners. There's a bit of theory and calculation involved. Easiest way ensure the condensers are good is to fit new ones. They're cheap to buy.
5. Check plug leads (if you can disconnect them from the coil). If they're the copper core type, you can simply test for continuity with your meter. If they're the suppressor type (some type of carbon impregnated core) test for resistance. It could be several thousand Ohms. I'm not a fan of suppressor leads. Different lengths of lead will have different resistances, and breaks in the conductor are not uncommon. I prefer copper core leads and resistor type plug caps.
6. Plug caps. Measure the resistance. Suppressor (resistor) type are normally 5,000 Ohms. Non suppressor will be zero ohms.
7. Make sure you have good spark plugs. If you have resistor type plug caps, use non-resistor plugs. NGK plugs will have an "R" in the designation if they're resistor type - BR8ES for example. A non resistor equivalent would be B8ES. I dunno about other brands of plugs. If you're using another brand you'll have to look up their ID markings.
I think that's pretty much it unless I've forgotten something (I'm sure someone will say if I have). If all that checks out you should have sparks.