There's really no mystery to it, so I'm not sure what you're trying to get at. Most depts have 3 Chiefs, some have 2, therefore x-1 = Chief of Dept, x-2 = 1st Assistant Chief/Deputy Chief, x-3 = 2nd Assistant Chief/Battalion Chief, or something similar to that.
But on the actual patrol car the mobiles can’t change.
Huh? Chief's cars are not referred to as "patrol cars" so that's a bit weird to call them that. Mobiles can and do change. From time to time vehicles get swapped between chief officers, or the mobile radio itself gets swapped between vehicles.