Here’s how a shifter works on an automatic transmission vehicle. I took one apart from my 2001 Toyota Corolla and made a video on how it works:


Here’s a few photos of the breakdown:
The lowly automatic transmission shifter:

Shift cable linkage in the car:

Its got a rod that connects to a pin. The pin engages with the black tab on the shifter’s ECU:


Shifter’s ECU determines if conditions are met to release the black tab (i.e. brakes are pressed, key is on, etc):


Solenoid itself moves out of the way of the black tab, allowing it to push downward.

On the other side, the pin engages with teeth, the profile of which determine if you have to press the button or not to pop it into gear. A spring keeps the position of the shifter:


Teeth profile:


Enjoy

 

Cool stuff.

Always wonder what would happen if I by accident slip my shifter into R while I was driving.

 

Not totally sure of how your Corolla is programmed, but, with many vehicles today, automatic-transmission shifters have a computer block-out that will not engage any gear that the computer determines will harm the engine or transmission, no matter how you move the lever. Buicks use a "Shift Denied" message that flashes on the display between the two large primary gauges. That not only prevents blockheads from shifting into Reverse at any forward speed greater than a few MPH, but also doesn't let one downshift too far at high speeds (or upshift too quick at low speeds)