I had a problem with the brake-shift interlock a few years back, it got stuck locked and I had to stick a screwdriver under the center console and wiggle it around for the manual release every time I wanted to shift out of park. Eventually I just took the thing out. Only side effect is I can shift the gears any time, car on or off, brake on or off.
While trying to fix it I learned that control of the interlock goes through a little box called the Instrument Interface Module. So here's a suggestion: unplug the connector for the IIM, and listen for your click when you usually get it. If no click when the IIM is unplugged, it's a good bet your interlock is the mystery clicker.
The O/D on-off switch on the gearshift also runs through the IIM but I don't remember what else. As a caveat I have never tried this myself.
To find the IIM: get under the steering wheel (try sitting on the passenger seat, lean over onto the driver seat (put the parking brake down!), then slide your head and torso under the steering wheel. Use a flashlight. Look far up under the dashboard, toward the driver-side of the steering wheel. The IIM is a green box, about 2" on each side. Except the side facing you is not green, it's black. The rest is green. Pull the plug. IIRC, it might be easier to take the box off of its' mounting bracket before you undo the connector. Can't remember exactly how to dismount it but I know it was a pain to reach it and work with it in that position.
