Nevermind. I inquired about your year and model, but I see that information now.
It looks as though you need a brake light switch.
Part number(NNN) NNN-NNNN which retails for $39.94
Here is the procedure
Replacing The Stop Lamp Switch Conditions
Removing The Stop Lamp Switch
NOTE: A number of clicks should be heard and felt when pressing.
Stop Lamp Switch, Installation
CAUTION: The stop lamp switch can only be installed in one way.
NOTE: The stop (brake) lamp switch will now be adjusted.
NOTE: The stop lamp must light when the brake pedal is pressed down more than approximately 1 mm .
Can this really lock up my gear shift like that?
No problem. No need to accept until you're comfortable with the answer. If the brake light switch isn't working, then your brake lights may not function. And you may still have the issue with the shift interlock not working properly. However, the car should be safe to drive.
However, yes, best to get it fixed sooner rather than later.