I think you're hearing other relays click - fuel pump and start circuit relays. At this point I believe you'll get the same response from the bike if you just leave it in neutral with sidestand down and the clutch out.
The bike uses two relays to fire the starter - start circuit/start switch relay and the starter relay. Neutral or the combination of sidestand up and clutch pulled in enables the start switch relay. Then when you press the start button the ground signal from it goes through the start circuit relay which lights up the engine light and should also enable/click the start motor relay. The start motor relay gets power straight from the battery so if it clicks, the starter should fire.
To check the starter relay, disconnect it - the plug with 4 wires and the two large terminals. Be careful with the red wire from the large terminal - it's directly from the battery. Apply power to Brown and ground to Blue/White on the relay. At that point you should hear it click. To complete the procedure you need to measure resistance between the two large terminals while power is still applied to brown & blue/white - should have continuity/very low ohms reading. If that checks out, I'd remove power and then measure continuity of the black wire that came off one of the large terminals to the starter motor where you jumped power to start the bike. Basically just checking that that wire has good continuity.
Edit: wanted to clairfy that in the procedure above that power & ground are being applied to the relay. As in, don't apply the power to the plug with 4 wires that was disconnected from the relay.
If the above is good, then the diodes would be next on my list.