For the first four years of my driving, I lived in a house on a hillside. The street was steep, and the driveway was even steeper. I still practice today the procedure that I learned 44 years ago. Although that is fewer years of driving than some of the others who have posted here, perhaps more important than the years of driving is the years put on cars. Of the three cars that I currently have, one is 21 years old and another is 23 years old. I have held onto some cars as long as 30 years of regular driving.
I agree with the article "When to Use Your Emergency Brake: Car Myths Debunked" that @Mike
cited above (post #5).
Specifically, I agree with the suggested order of things to do when applying the parking brake. "When you park your car, put it in neutral, set the emergency brake, then release the brake pedal. With the emergency brake holding the vehicle, put the transmission in gear or “Park,” and shut off the car. It reduces pressure on the clutch, transmission, parking pawl and CV joints — and reduced pressure means reduced wear."
I have always made it a practice to
1. Put my foot on the service brake pedal.
2. Shift the transmission to "neutral".
3. Set the parking brake.
4. Release the service brake pedal (The car may roll about an inch downhill as the downhill force being exerted by the car is transferred to and then held still by the parking brake. The parking brake is better suited to hold the car from rolling downhill than the parking pawl in the transmission. This also allows you to ensure that the parking brake has been applied firmly enough to hold the vehicle.).
5. After I have verified that the parking brake is holding the car, I quickly shift the transmission from "neutral" to "park".
I have known of more than one person who just used "park" and never set the parking brake who also eventually had their parking pawl break in their transmission. That is an expensive repair.
In the 5th step of the procedure that I have outlined above, I usually keep my foot off of the service brake pedal while shifting from "neutral" to "park". If it is done quickly enough, the vehicle will not shift into "reverse". However, on all of the later model Chrysler vehicles that I have driven that have the rotating knob on the dash to shift the transmission, when your foot is off of the service brake pedal and the knob is in "neutral", you cannot rotate the knob at all until you put your foot back onto the service brake pedal. Thus, for these vehicles (including the 2017 Chrysler Pacifica Hybrid), I would have to change/add
5. After I have verified that the parking brake is holding the car, I reapply the service brake pedal with my foot.
6. Quickly shift the transmission from "neutral" to "park".
I think that it is interesting to note that on most heavy duty trucks and buses with an automatic transmission, there is no "park" position on the shifter. To park, you shift to "neutral" and apply the parking brake. The parking brake holds the heavy vehicle from rolling downhill, and the parking pawl in the transmission cannot be broken because there is no parking pawl in the transmission.
Regarding the possibility of air leaking out of an air brake system when a heavy duty vehicle is parked for an extended period of time, virtually all of these vehicles have a parking brake that is a spring brake system. A very strong spring is inside each parking brake canister. When the parking brake is released, air from the air brake system compresses the spring in each parking brake canister so that the spring releases the brake and the vehicle can roll. When the parking brake is applied, air is allowed to escape from the parking brake canisters, and the strong springs apply the parking brakes. When the parking brake is applied, it is the strong springs in the parking brake canisters that are holding the parking brakes in the applied postion. Thus, if the vehicle is parked for an extended period of time and the air slowly leaks out of the air brake system, the parking brakes will still hold the vehicle, because it is the springs that are applying the brakes, not the compressed air.
To the best of my knowledge, my Pacifica Hybrid is still sitting in the storage lot in Taylor, Michigan. So, I have not had an opportunity to explore how the auto-apply feature of the parking brake on this vehicle operates. If it applies the parking brake automatically when the transmission is shifted into "park", it seems to me that there would be a chance that on a hill some of the downhill force of the vehicle could be allowed to be placed on the parking pawl in the transmission, because, after the transmission has been shifted into "park", the vehicle might roll downhill when I remove my foot from the service brake pedal. If the vehicle rolls a little bit downhill in this scenario, there will be some pressure on the parking pawl in the transmission. If that is the case, and if there is a way to disable the auto-apply feature of the parking brake, I would probably disable it and then just follow the steps that I have outlined above.