AirTag searching for signal
I have an AirTag for my dog and it’s constantly saying it’s searching and to move to another location…
AirTag
The Apple AirTag relies on a Bluetooth beacon to transmit its location information to the Apple Find My Network. In turn, it relies on an iPhone (yours or someone else's) to be within Bluetooth range (~30') to receive this information.
This phone, if it has an active Internet connection, send that information to the Apple servers. This is where you would "see" the tag's location with the Find My app on your phone.
To be "successful" a number of things must occur, and any one of those not working could be the reason you are seeing that message.