In my dept. here on LI, when you first join you are on probation. It could be anywhere from 6 months to a year. During your probation time you are not allowed to have a light (Here on LI it's a green light).
Once you are off probation and are now considered a regular member, you can have green lights on your vehicle. The green light is not exclusively for responding to the building, but also if you are responding to the scene.
As a probationary member you are not allowed to respond to the scene, as a regular member you can. Also probies rushing to respond to the building without any regular members being there doesn't accomplish anything, as without a regular, the ambulance isn't going nowhere. So there is no need for probies to have a green light.