Having GPS in a work vehicle that is part of work is fair game, but there would be privacy concerns having GPS in a vehicle that is included in a remuneration package.

Would the same apply to company issued mobile phones?

We had an incident where a person who was legitimately monitoring their fleet vehicles on GPS noticed another manager's vehicle was parked at the residence of another staff member. The person insinuated there was 'something going on' when in fact he was doing some 'odd jobs' in his own time. This resulted in us writing a policy for information security and privacy. Tony, you contact me directly if you wish to have a copy. Email: brianpatmacmovedotcodotnz

Doesn't the company have some level of responsibility for the vehicle usage, even if it is being used in a private capacity? In this case, I think that the privacy concerns are reasonably taken care of through a well-written policy (as long as it is practiced).
It is reasonable to have it in a work vehicle, but IMO it isn't reasonable to expect it to be turned off outside of work hours.

Thanks for your comments folks, I've learned a bit more after canvassing this topic.

I've heard that companies that treat this as a safety issue, and not a speed monitoring issue, are able to get this across the line (external fleet manager and drivers get their own report - no-one in the company sees it unless there has been multiple overspeed incidents).

It has become self-policing, with employees making a competition out of it eg division with lowest/no speed tickets etc. There was some initial grumbling, but trust has built to a point that they're now discussing the real time monitoring as they've seen how the driver feedback reporting helps them improve their own vehicle handling. The employees are behind it as they and their colleagues often work alone, and outside of cellphone coverage, so they get the benefits of location monitoring during work hours.

Like most things, its a process, and its about building trust first...

Like most things, its a process, and its about building trust first. — Tony Watson

And that's the key.
I find these debates interesting, coming from the aviation industry, where voice recording/location monitoring is expected, and even wanted by staff, even when not legally required. I just cannot understand the resistance to things like video monitoring in trains, etc.