Initiation of systems without input. i.e., engine, radio, sun roof, etc starting, opening and/or engaging without input from an operator.
Attacks and/or damage by animals and/or creatures who's identity and genetic origin is without a scientific example recorded elsewhere. No one will believe you either.
Entities showing up within headlight range, possibly even in the road, then disappearing without being run over.
Unexplained scents, movements, etc, within the interior of the vehicle.
An unexplained draw to odd places, i.e.:
breaking down in front of an alligator farm;
long stretch of lonely road with no cell tower within range for help;
in front of isolated boot hill cemeteries;
off ramp of busy highway during 5 o'clock traffic, with perhaps half a house being hauled on a truck behind you; unexplained apparitions of passengers who appear and disappear within the confines of the vehicle.
Many other examples exist, yet are too numerous to list here. If you can identify with one of these situations, you can, most likely, add an odder descriptive from your own experience.