Yes, you should feel/hear the detent solenoid working in the console when you step on the brake in park with the key on. With your hand on the shifter you will feel it clicking when it operates. The switch down at the pedal is fairly simple, just a spring loaded plunger switch that rides the brake pedal rod, so that when the pedal is pressed the plunger pushes out and the circuit is completed, energizing the shift detent solenoid so you can move the shifter button. Once in any gear but park, the solenoid's operation is overrridden so it doesn't work needlessly every time you press the brake while driving.
I don't know if the shift detent switch is integrated into the other functions controlled by the brake pedal....usually brake light operation and cruise control cancel are on one switch, so it could well be included in one multi-function pedal switch, I don't know, haven't run into trouble with one on a Lumina yet...
Another possibility is if something sticky got spilled into the console, it could be interfering with the solenoid or detent gate operation, this happens sometimes too...a simple cleaning will correct it, but I'd think the first guy would have seen this if it was the case...