Apple TV control panel not finding Apple TV Box

The software remote in Control Center on iOS devices will work with Apple TV (3rd generation or later). Unfortunately, that excludes the 2nd generation.

Set up the Apple TV Remote on your iPhone, iPad, or iPod touch - Apple Support

“The Apple TV Remote in Control Center works only with Apple TV 4K, Apple TV HD, Apple TV (3rd generation), and AirPlay 2-compatible smart TVs.”

Identify your Apple TV model - Apple Support

Second generation will have “A1378” on the bottom of the device and in Settings﹥General﹥About﹥.

Third generation will have “A1427” or “A1469” on the bottom of the device and in Settings﹥General﹥About﹥.

The web page Check your service and support coverage - Apple Support will get a device identification from a serial number. (It will probably also say support is expired, but then you already have the details that you wanted.)