It engages in park as in it's not rolling but the red P doesn't show up unless I hold the button on the stalk down for a few seconds. It's been like that in every tesla I've owned or driven.
Red park symbol:
The long press also activates the parking brake, for use if the service brake fail (will stop you while moving)The parking brake indicator lights up
on the instrument panel whenever
you use the touchscreen to manually
apply the parking brake.