Make sure the fuses are good. A test light may be needed to check the light circuits for power to see where there is a power loss.
brake switch located on the top of the brake pedal
2006 lincoln navigator requires a 7mm hex to remove brake caliper
Turn Signal / Brake Light Troubleshooting (check in this order): 1. Check Fuse 2. Check Bulbs 3. Check Flasher Relay 4. Check Turn Signal Switch in steering column and/or Brake switch down by brake pedal. Most likely its the fuse or bulb. See sources and related links below for bulb information.
the turn signal switch is probably bad
Fuse
If you have the same bulb for brake and signal, brake light power needs to be interrupted by the signal lights, The brake circuit has to go through the signal light switch so the problem could be there.
Since most brake/turn use the same filament in the bulb(1157) then if the turn signal switch is bad or offset then it will effect the brake lights.
The lights wiring is grounded and you might want to check to see if the ground is connected properly to the frame.
On a 2004 Lincoln Navigator : Starting on ( page 244 ) of the Owner Guide it explains the Brake Shift Interlock and what to do if you cannot shift out of PARK ( you've already done that ) Check to see if the brake lights are working , or it is possible that the fuse for the Brake Shift Interlock has blown and is no good
Check and make sure you have the correct bulb. The turn signal/brake light is a dual element bulb and if you have a single element it does not work properly.
According to the 2003 Lincoln Navigator Owner Guide : Yes , it has an automatic parking brake release
Tail lights. Brake lights. Backup lights. Signal lights. License plate lights.