The two small terminals, which down here we call triggers are not polarity sensitative , Just so long as one is + and the other is - it will work.
Some models the - is made with a short wire to the frame while others will run through some of the safety switches to ground.
This is typically found on ZTR's and John Deer who like to really complicate things bu putting a relay in there as well.
So customers come in here telling me the solenoid was bad, they replaced it ( sometimes more than once ) because when they bridged the hot wire to the trigger wire the solenoid did not close but they never checked for a ground on the other wire which like the magneto wire can be ground or open.