It does seem like that's an element, then -- this is not to say that it's sufficient for anything, since obviously a sufficiently good record of where one goes on public thoroughfares would fail the same test ('reliably reveals that so-and-so went to visit a specialist doctor, divorce attorney, and brothel all on the same day')
Which, I would say, does seem a lot less black-and-white than the cell phone example, and anyone who thinks it's all settled now might be in for a surprise.
Automobiles are not cellphones, and the state is free to regulate automobiles. It could mandate tracking devices in all cars, if there was political will.
https://www.thedrive.com/news/license-plate-cameras-will-soo...
United States v Jones already answered this question.
A vehicle is literally considered an extension of your body, and this has been held up many times, starting with Carroll in 1929.
More recently, the 9th circuit put forth a ruling vacating a man's conviction because a cop merely touched the vehicle, thus triggering a warrantless search complaint.
There's a lot of case law that goes against what you're thinking.