It likely goes to the mower side of the harness to the solenoid.
You can put a 12 volt test light on it (light grounded), and turn the key to
crank.It should light up if I'm correct.
The solenoid either has two small wires, or one small wire to it.
The second wire is ground, on the 1 wire solenoid, the solenoid grounds itself to the frame(no need for a second small wire.
.