Are you sure it's your brake lights and not the tail lights?
Your brake light switch could be bad, have you checked the brake light bulbs? (assuming it's the tail lights you are seeing on)
Any bulb out message in the cluster?
The other possibility is the LCM.
All external lights are controlled by the LCM. If your lucky it's just a random bit error in the LCM module that you may be able to clear by disconnection the battery after the 16 min timer shuts down all of the modules and the trunk light goes out.
Disconnect both cables from the battery and connect them together, then turn the ignition key to the run postion for 10 min.
After 10 min turn the key off and reconnect the battery, positive lead first. If your lucky your problem will be fixed. If it isn't you will probably need a new LCM, it will need to be coded.
Used LCM's can't really be used, they store the VIN and mileage which won't match what is stored in the cluster and DME. This will set off the Tamper light next to the mileage readout in the cluster.