They make a GPS tracker for trailers.

This would be what I would use on a classic car if I had the need. They have their own long life battery, that gets tied into the trailer/vehicle power feed to maintain as needed. but if the main battery is pulled from the trailer the device battery keeps sending that signal.

The device and battery are small, and can be user mounted in just about any location, they come in a weather tight box. so under frame mounting is a popular choice, and easy to hide from anyone poking around.