Using the GPS signal to detect motion is the most power-expensive path though.
The cheapest in terms of power consumption is a simple Accelerometer/Gyroscope component.
The difference can be months or even years in longer battery runtime compared to GPS.
Put it in an RF chamber and keep another GPS receiver outside the chamber some distance away to make sure it doesn't lose lock on the real satellites. That's your leakage canary.
We had one of those in an underground parking garage for autonomous vehicle testing at a previous job, but it was a naturally really well shielded room, and it was just repeating surface signals so no one would complain.
Bluetooth beacons would need to add an accelerometer, but that undermines their use in pinpointing an object at rest.