It is possible to do, but might cause confusion to other drivers, who are expecting that to be a "brake light" only, so I personally would never do that!
You can make it stay on all the time with the lights on but there is no easy way to make it act like a the normal brake lights (come on dim and get brighter when you press the brakes) you could buy a resistor set-up to do this but it would be hard to get it right. If you want it on all the time with the lights on just wire the BN wire going to the brake lights into the DG wire going to the 3rd brake light. It may burn the lights up a lot faster though. Just make sure you cut the BN from its original harness so it doesn't try to add more voltage to the light when you press the brakes. That could cause some damage. Let me know if you need any more help.