Reddit mentions of Donner Electric Guitar Amplifier 10 Watt Classical Guitar AMP DEA-1

I've set up similar with an automation app for makeshift motorcycle and home security before. There may be better options available to a rooted phone that I'm not familiar with.

You could go the easy route and use Google's Find My Device, which allows you to remotely update the location pull and set off a tone. Or, you can build one in an automation app (Tasker, AutoMate, AutoMagic), which allows sensor use—I can't guarantee reliability with your phone, but I've had good results. The real problem, I'd imagine, is how would you delay their discovery of the phone long enough for the tracking to be of value? Maybe you'd get lucky and they'd drive home without opening it, but that's a high level of stupidity to count on. For this reason, I'd imagine a security camera would have a better chance of catching them—though that leaves the problem of identification. But, if you are dedicated to this, I'd suggest getting an item you can hide the phone and battery pack in (securely—no rattling) that someone wouldn't think to disassemble, is worth keeping, and will function believably (if tested) until you get the cops there. Maybe a small amp for a guitar? Pop off the back, adhere it to the case, close it up… Whatever it is, it'd have to be believably packaged and labeled for shipping—unless, again, you're counting on their incredible stupidity. Anyway, I'll skip to the phone portion and leave the rest to you.

Here's a manual version in AutoMate, which requires you check its location via text. You could easily switch it to send automatically based on time or a sensor reading (movement, geofence, magnetic reading, driving detected, etc). Or, if you feel like gambling and letting them find the phone, burst pictures that upload to Drive when the phone is exposed to light, or whatever. If you have something specific in mind, or need help getting something working, feel free to message me.