If you want to go "auto" for the vast majority of 12 volt jobbies then you will need an adjustable pressure regulator and switch.
The reg will have to be adjustable so you can set what pressure to inflate the tyre.
The switch will be to turn off the Compressor.
If you don't have that the compressor will just run it's guts out while you are dicking around elsewhere and not needed and either overheat or exceed it's duty cycle.
The reg is easy but the switch set up would be tricky