My latest project for the X3 reverse involved switching all the turn signals out to LED lights. I upgraded the X3 reverse lights to LEDs as well, and wrote up the procedure to do it yourself below.
That gap between the tailgate and plastic interior cover is where you need to make your attack
How to get at the lights inside the tailgate of your BMW X3
The biggest factor to accessing the X3 reverse and brake lights in the X3 tailgate is having the right tool. I highly recommend this trim tab removal tool
I purchased on Amazon.com since there are close to a dozen plastic tabs you need to unsnap to access the tailgate lights. I purchased the tool, then opened the tailgate in my garage to a point that made it easy to access the gap between the outer tailgate and interior plastic cover. 
Looking in the X3s rear tailgate – the bottom of the plastic panel is still attached to the bottom of the tailgate. Notice the pointy plastic tabs that click together and must be unsnapped
Separate the interior plastic from the tailgate
Now use the trim tab removal tool
you purchased and start popping the tabs apart. You don’t have to completely remove the back panel to access the lights, start on the sides halfway between the back window and bottom of the tailgate. Shimmy your tool in, spread gently and peak in the gap. I did this a few times and “felt” around with the tool where a clip is. Get your tool close to the clip then give it a good squeeze to pop the plastic tab apart. Continue reading on page two >>
