There are only two screws that hold the fixture in place. Once you remove them, the fixture will push out. It is a tight fit though so you need to push it out from the side that the lense is on.
If you want to reduce your labor, you can just cut the wire going into the brake light right at the fixture and then strip the ends and solder them to the LED strip. You may want to put a connector on instead so that you don't have to solder it in place.
I actually removed the Brake light fixture along with the wire, but to do this requires that you pull back the ceiling gasket in the back and pop a couple of fasteners that hold the ceiling in place so that you can unplug it. There is also a grommet that needs to be pushed through to remove the wire and connector along with the brake fixture. It's not worth the effort.
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