GPS is passive. It isn't like the GPS sats are going to signal back to some receiver where another receiver is.
You need some means of transmission between the tracker and it's receiver.
Cell doesn't usually need much power, and is wide-spread, but you do have to rely and pay for external services.
Wi-Fi has pretty good distance, and if you are using point to point Wi-Fi, you don't need to rely on external services.
However you were already using Wi-Fi (or Wi-Fi band) and lost it so a separate tracker might not be any better.
BT doesn't cost anything to operate, but it is short distance. It's worse than Wi-Fi, which you already had with the AC itself and lost.
The Wi-Fi and BT could be better in that they may still operate when the AC isn't, and you'll pick up their signal once you get in range with your receiver, if you manage to do so.
Wi-Fi could do both, find an open Wi-Fi with internet so your receiver or app can get the location via internet connection, and it can connect directly to your receiver when in range if internet connection was not available.