Low voltage to cyl 1 & 4 coil

[FJlemonrevival]

Good day everyone !

A friend of mine gave me his father's FJ1200 to put it back on the road. The man passed away more than 20years ago and the bike has not started since. It's a "1WH" model (it's french, so maybe there are some differences with the US ones).

Here is my problem : cylinders 2 & 3 get a weak spark, cylinders 1 & 4 get no spark at all.

When I turn the key, the right coil (1 & 3) receives 11.3 volts, and the left one only gets 0.53 volts.
For that reason, I don't think changing the coils alone will solve the issue yet.

The left coil is wired with an orange cable (shared with the right coil) to the ignitor box, and to the main relay with a red and white cable. The latter seems visually in good condition so I suspect that the relay is bad.

Anybody knows how to test that relay ?
What wiring connections would you check ? (in case I forgot one)
Any chance some other system/sensor is interfering with the signal ? (like the fuel reserve for example)


Thanks in advance for your help ! 

PS :
The battery is new and puts out about 13v
I tested the coil's power supply with the coils disconnected.
The big ground cable at the back of the engine is clean and corrosion-free