The problem with your light isn't on the power wire side of light. If it were you'd be blowing fuses. The problem lies on the ground side of the light. Something is shorted to ground and causing the ground side of light to be grounded all the time. That is why bulb is on all the time.
The door switches provide a ground for dome light when door is opened. As does the light switch when turned to dome position.
To test door switches, simply unhook the wire from the door switch. If door switch is grounded all the time causing light to burn, it will shut off when you remove the wire from it. Kick panel must be removed to get to door switch. Do both door and see if light goes off.
Unlike the camaro, the firebird has a separate light switch for the interior lights. To test it, simply remove the black wire from the switch. If there's a connector there with all wires remove connector from switch. If switch is grounded all the time, this will shut off dome light.
If removing wires from either door switch or light switch turned your dome light off, replace the offending switch.
If this did not turn dome light off. the problem is either the dome light assembly itself is grounded, or the wires that go to door switches or light switch have a short to ground.
You can test the dome light itself by simply removing the assembly from the roof. If light shuts off with assembly not touching the metal of the roof. There's the offending party. If light keeps burning with dome light hanging, your problem is with the ground wiring being shorted to ground somewhere.
Unlike a short in a power wire, a short in a ground wire doesn't hurt anything. It just keeps the light on all the time power is applied. Since dome light is powered at all times, light will stay on all the time and run your battery down.