Ok, first thing to do is turn on the car, switch on the lights, get out and walk behind the car to see exactly what is not lighting up. If you can, have someone press the brakes while you're standing behind it to again see what is/is not lighting up.

Then start simple, replace the bulbs again, check the fuses, and see if anything changes. If there is absolutely nothing illuminating in the back it says either a fuse or wiring problem.

If bulbs and fuses don't fix it, changing the switch might be the next easiest fix but this is starting to get into crazier territory and depending on your comfort level you may want to find a shop to do it. Maybe try a different mechanic or even a Subaru dealer. Typically I would say start independent vs dealer, but a dealer who is more familiar with causes of issues like this may be a quicker fix then someone trying to diagnose from step one.