The Y/R wire from the START button is the "ground" signal sent to the solenoid. At the solenoid, you should have a thin BLK also, that's the power to that "relay" when the Y/R is pressed, it completes the circuit of power (BLK-power, Y/R-earth) this lets the juice flow from the stud that connects to the battery POS (right side stud) to the Starter motor (left side stud).
If you have confirmed that the solenoid turns the starter motor, then you can easily test the START button. From the solenoid, disconnect the Y/R from the harness, and touch the bare end (male bullet connector) to frame ground (Key ON please). This should spin the starter motor (be sure bike is in NEUTRAL). If this activates the Starter, then somewhere between the switch housing and the solenoid the Y/R is incomplete.
At the housing, the end of the Y/R should have continuity to Ground with the housing fully installed. Meter set to "continuity" touch either probe end to the bare wire, and the other probe to the chassis. Get a tone? If so, move along through the harness repeating the trace of this Y/R wire. When you stop getting a tone, you'll know where along the path that the Y/R is disconnected or broken.
You can also perform a similar test on BLK. But this time you set your meter to 12v and ONLY the RED probe these the BLK wire. With Key ON, RED probe to BLK wire, Black probe to GROUND, do you get 12v? Check each connection after the headlight, at the solenoid, the BLK/WHT wire for the ignition coils, and so on.
Repeat this step (voltage) on Br/WHT. Br/WHT gets 12v from the key switch when turned 1 position and it feeds your auxiliary lighting functions.
You stated earlier that the Horn worked, but only in position 2 (aux or parking). It should also work in position 1 ( position 0 being OFF). If not, you have a wonky key switch I'm afraid.
Take your time reading through this, complete each step, then proceed patiently to the next. As long as your meter is set to 12vdc, you must only use the RED probe on the colored wire, and the BLACK probe on GROUND or solid GREEN.