With truck running and foot on brake, it would not disengage out of the park postion on 2006 Lincoln Navigator

Truck with engine running and foot on the brake will not
disengage from the park position,unless you take off the
silver trim accent surrounding the gear shift lever & push
in the overdrive mechanism.

Asked by for the 2006 Lincoln Navigator
Check your brake lights - are they working? Very likely not. The brake light switch on the brake pedal is likely faulty. And / or the wiring connector at the switch. Check there first.
Brake lights are working.
Dave had a good suggestion, that's the first thing to check.
Since the brake lights are working, check the shift interlock solenoid. It might failed and stuck in a closed position, locking the shift lever.
You can find great repair manuals with step-by-step instructions, diagrams, parts locations and other important information here:

Where is the shift interlock solenoid located in the 2005 Lincoln Navigator/
1 more answer
Why is the vehicle continuing to do this even after you return it to Park?