Cant help you out much, but I can help you get a tracking device. Go to:
www.centralplainsgps.com

GPS trackers aren't cheap, $300 or more, so he'd have to be really
serious.

The devices are usually small enough to fit in the palm of your hand,
and these "trackers" are usually attached to the car by magnets.

Your ex would need access to the car to put it inside or under the
hood, does he still have keys? That leaves anywhere under the car.

I can't see why the maker would have it emit any audible noise, seems
counterproductive to a covert device. Unless the signal is causing
interference with something in the car.

Perhaps a mechanic that you trust (who had no personal or business
relationship with your ex) could look around under the hood, fender
wells, undercar for anything that didn't come from the factory. They
sell devices that can detect these things; I found some on
cuttingedgesecurity.com but they're a couple hundred also. Perhaps it's
worth paying a local private investigator to scan your car.

The whole idea of a snooping ex-spouse is creepy.