Mr BRR, here is a drawing i made with the help of one of "the team's" diagrams and recognizing all their input.
From what you describe it points to the start switch itself OR the wiring to it including the diode block and the start motor relay, the start motor relay is supplied from the start button which gets it's supply from the engine stop switch.
A; If the instruments sweep that indicates the key switch is working,
B; if the fuel pump initiates that indicates the "engine stop switch" is working and
C; if the neutral light is on that means the bike is ready to be started.
The clutch switch and the sidestand switch only stop the bike from being driven with the stand out and the engine will stop, this seems not to be the problem in your case and is a separate electrical circuit.
The clutch and sidestand are in parallel and either one can ground a pin ( b22 ) to the ecm and if both are open the ecm recognizes a potentially dangerous situation and then kills ignition if the bike is not in neutral ( pin b33 ) Not shown on this drawing which i made to be read a bit better than the complex wiring diagram.
Hope you can understand european symbols with their explanation and the current flows from the battery at the top to the bottom through all the parts.
The bank angle sensor stops the electrical supply to the control circuit and stops the engine if it has fallen over to stop the wheel from spinning, it is not the cause of your particular problem but i have drawn it to better understand the working of the engine stop relay.
The function of the diode block is to combine the neutral light indicator separate from the starting circuit, so although they are connected together they function separately without influencing each other, the diode block is located beside the fuses and relays under the seat and normally does not need attention, it is removable by pulling it up like a relay and maybe reversible if the pins allow it.
Hope this helps to locate the intermittent issue.