Due to limitations with the Apple TV you are only able to pair 2 Bluetooth devices directly to the Apple TV. If you have more than 2 Bluetooth devices they must be paired through the companion app.
At present there is no way to manually switch from using the Apple TV Bluetooth to the companion app. The only way to start using the companion app Bluetooth is to attempt to pair a 3rd device through the Apple TV, at which time a dialog will appear providing the option to use the companion app.
The drawback to this approach is that once the attempt to pair the third device to the Apple TV is made, the device is committed to the Apple TV and will not be seen by the companion app, leading to “No Signal” issues.
The workaround is to remove the battery from the 3rd device and wait for it to timeout, dropping its connection to the Apple TV, at which time you can replace the battery and pair it to the companion app properly.
If a button were provided to manually choose to use the companion app for pairing then the need to remove and replace the battery in your Bluetooth device would hopefully be eliminated.