You're not wrong at all. You could easily install a manual pushbutton that you could toggle. Things get a little more sticky when you talk about having a relay controlled pushbutton. Depending on your vehicle, you may have to take things into account such as power draw when the vehicle starter is on; timing of the pushbutton, and how to keep the PC alive while the PC is shutting down.
My obvious recommendation is to use a "smart" shutdown controller