1990 LX going into park sticks when cold

[dex3703]

I have a 1990 Civic LX automatic with 257K miles. It has a problem that when it's cold, the safety interlock keeps the gearshift from going into Park. The transmission goes into park properly, but I'm guessing the interlock that makes you press the brake to shift out of park doesn't engage. The red P display in the dash doesn't light up, and you can't turn the car off. Massaging the brake and pushing the gearshift up against the park position seems to help a little.

What parts are involved and how do I fix this? It only happens when cold, In the summer it's fine.

Thanks in advance,
Derek