I am not sure how the e-brake works. It may be spring loaded on and needs power to pull the brake off so things can turn. Or it could take power to apply the brake and no power to the brake circuit means no brakes.
Spring loaded apply would be the safest method.
Looking at the first diagram it looks like you have to push in a button to engage the e-brake. As soon as the e-brake button is released the e-brake is also released.
Does pushing in the e-brake button make the contactor move?
Bill D