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It just snaps in the top. Take a small flathead screwdriver or trim removal tool, and pry up on the lower back edge.
Once it pops off, you can access the push button.
When you say moves more slowly, I'm hoping for you that it isn't caused by a weak Park solenoid microswitch failing, and not releasing the park locking pawl completely.
That is what happened to mine, and I did what you are now doing. Eventually, the shifter got stuck in Park, then I got it out of park and it wouldn't return to park.
I had to take the console off, get to the locking pawl and tied it back to prevent it from ever getting stuck in Park again.
Automatic Shifter Button
