Pairing the device
After you add a TV, restart Homebridge. The plugin connects to the TV and the TV asks for permission. When you allow it, the TV gives the plugin a token. The plugin saves it and uses it on every later connection, so you only allow it once.
When the prompt appears on the TV, choose Allow.

The TV has to be on for the prompt to appear. If it is off when Homebridge starts, the log says Waiting for the TV to turn on to pair.... Turn the TV on and the prompt appears. You do not have to restart Homebridge.
If the TV does not answer in time, the plugin tries again a few times. If it still fails, the log says Pairing failed, it will be retried the next time the TV turns on. Turn the TV off and on again to get a new prompt.
With debug mode on, a successful pairing writes Device paired with success in the log.
Clicked Deny by mistake
Deny is remembered by the TV, and later connections are rejected. The log then says TV rejected the WebSocket connection (unauthorized).
On the TV open Settings → General → External Device Manager → Device Connection Manager → Device List. On newer TVs the menu is General & Privacy instead of General. Look for Homebridge in the list, and either change it to Allow or delete the entry. If you delete it, the prompt appears again the next time the TV turns on.
Frame TVs
A Frame is detected during pairing. Its Art Mode and Power switches appear once the TV is paired. See Frame TVs.