The behavior you're experiencing is expected, and it comes down to how Apple's Find My network operates.
AirTags do not have their own Internet connection, GPS receiver, or Wi-Fi capability. Instead, they periodically transmit Bluetooth signals that nearby devices participating in Apple's Find My network can detect. Those devices can then securely and anonymously relay the AirTag's approximate location to Apple's servers.
Consequently, having an Internet connection at your second home is not sufficient by itself. There must also be a compatible Apple device nearby that can participate in the Find My network.
Regarding your proposed solutions:
- Mac mini: Although Macs support Find My, I would not recommend purchasing a Mac mini specifically for this purpose. Its ability to act as a reliable, continuously operating AirTag location relay is not something Apple documents or guarantees.
- iPhone 6s: This may be worth experimenting with if you already own the device. The iPhone 6s supports iOS 15, which includes Find My network functionality. However, I would not assume it will reliably relay AirTag locations while left unattended, particularly over extended periods. Its aging battery is another consideration.
- A newer Apple device or home appliance: Apple does not currently offer a dedicated AirTag location relay or hub. Devices such as HomePod and Apple TV should not be considered substitutes for a nearby iPhone participating in the Find My network.
My recommendation would be to test your existing iPhone 6s before purchasing additional hardware. Connect it to your home's Wi-Fi, enable Bluetooth, Location Services, and Find My network, and leave it powered on near the AirTags. Then, while you're away from the property, monitor the AirTags' reported locations and timestamps in Find My over several days. This should help establish whether the arrangement works reliably in your particular environment.
One important limitation: AirTags are designed primarily for locating misplaced belongings, not for providing continuous or scheduled location updates. Even with a nearby compatible device, there is no guarantee of how frequently their locations will refresh. If you require dependable remote monitoring of belongings at a fixed location, a dedicated monitoring solution may be more appropriate.
Apple explains how the Find My network operates here: Use Find My to locate your lost Apple device or AirTag