shift position Park not moving EZ

On 2002 Lincoln Town Car, last week I had an issue with the ignition lock cylinder not remaining seated properly and causing the inability to get to the " RUN " position or " Start " position.

I still have that same issue about 1 per week if I am not careful when turning the key " OFF " and be gentle with the ignition lock cylinder.

Now, when I get the ignition to " Start "....when I try to take the transmission out of PARK....it will not
move to any other shift position.

If I wait about 10 seconds for the computer systems to process, sometimes I can then have access to making the transition from Park to any other gear positon.

Moving the steering wheel or other minor steering column " jiggles " do not seem to have any effects.

Any thougts about the transmission " sensor " or shift linkages....?

Here's a clue, the "Lighting Control Module" under the dash can affect the operation of the shift lever. I bought a used LCM off eBay to fix my headlights. It was the wrong year for my car and would not let me shift out of park once I started the car. It did however fix the headlights, I just could not leave the driveway!