Both methods are really the same, they both result in more current to the solenoid.
The solenoid would like 40 - 45 Amps but Guzzi put it on a starvation diet.
http://www.thisoldtractor.com/guzzi007/schematics/2008_Stelvio.gifIf you start by looking at the starter (25) you see just a simple box, this is ok to represent the starter but it gives you no idea how it works, the solenoid that sits on top is actually 2 coils. one that draws 11 Amps, the other will draw 40 if its fed 12 Volts.
The two coils working together make a very strong electro magnet that pulls the starter gear into mesh and closes the main contact to send 150 - 200 Amps through the starter and spin the motor over, the problem is to get enough current through the solenoid coils to let them do the job they were designed to do.
An easy way to prove the starter out is to replace the wire on terminal marked (1) with a few feet of 16 gauge wire, if you make sure the bike is in Neutral (pull the clutch in for good measure) then touch the other end on battery positive, you should find the starter pulls in with a real clunk and you get quite a spark on the wire when you break the circuit, that's caused by the electricity stored in the 2 coils.
I don't know what size wire they use on the Stelvio but my 07 Griso had something equivalent to 20 gauge.
Use the great Carl Allison drawing I posted and trace the wire back from the starter solenoid all the way to its point of origin the battery. You will see the wire comes in this case from a pair of relays 3 & 4 (most Guzzis only have 1 relay) but ignoring that for the moment trace the wire internally through the coil you will see it goes to a contact and the other contact ends up on a Yellow wire.
The yellow wire works its way across to the ignition switch and also a branch goes down to fuse 2 and from there back up via a Green /Black to the ignition switch. Another branch of the yellow goes to the Number plate light 20 and a Glove Box Relay, we will get back to that.
From the ignition switch theres a couple of Red/Yellow wires that combine and finally work there way down to a main fuse at the battery.
You might wonder why the electricity can't find its way from the Red/Yellow wires at the switch to the Yellow wire and straight across to the Start Relays, I wondered that but I don't believe there's a contact in the switch as its shown, the electrons have to go the long way around via fuse 2.
By the time the electrons find their way back and forth they are feeling a bit weak and on a good day they will find enough energy to pull the starter into mesh, on a bad day the solenoid just sits there pulling 15 - 20 Amps without moving.
The idea of relays is to boost a weak signal and make it strong or isolate signals of different Voltage from one another. In this case its to make a weak signal strong, that's hard to do if the power supply is weak, So what we do (the MPH kit does this also) is make sure the relay has a good strong power source.
I suggest you purchase a roll of 16 Gauge Yellow wire and connect it to the two relays, just snip the existing wire before it splits and crimp it to the relay end with a butt splice or by soldering if you prefer. At the battery provide a 20 Amp in-line fuse.
So now you have a 20 Amp fuse to yellow wire to the two relays, from the two relays the existing wire should be sufficient to feed the solenoid but if it looks too small you can boost that up also either with another in parallel or replace it with a No 16.
This wiring change makes no difference to the start logic, it still won't crank with the key off.
Getting back to the yellow wire feeding the number plate light, I believe this is to allow for turning it on while parked, that's why it goes to the switch, for the park position, but interestingly if you look at the plate light it will give you an indication of the voltage at the start relay. I suspect you were to watch it when the starter hangs up it will go from full brightness to quite dim indicating low Voltage.
When the starter actually has enough energy to engage the current through the coils drops to about 1/4 and the Voltage will shoot back up.
A typical starter with a good power supply will engage and start working in about 15 milliseconds but with a weak supply it might take 50 to 100 or not at all.
Its important to insulate the other end of the yellow wire so it cannot short to chassis because it's used for other functions less demanding.
I suspect if you were to dismantle the ignition switch and clean the contacts it would also restore the starting but it will always be a weak link.
I may be wrong but I suspect the Moto Guzzi factory think the starter solenoid only draws about 10 or 11 Amps, thats all the current you would see while the starter is cranking over, Its the inrush current too quick to measure that causes the solenoid to fail and fuses to blow. The more power you feed the solenoid the less it uses because it works faster.
Would you be happy if your Guzzi was just running on one cylinder, then why put up with a starter that's only half working?