Yes black and brown together. I always check with a voltmeter or test light to confirm if I am dealing with old trailers as many times previous owners have spliced in parts of the wiring.
My trailer had three connections between the vehicle plug and where it went into the front of the trailer.
Each connection is a place for corrosion and poor connection.
The fourth wire may be your backup wire.
plate light can be added and connect it to your running lights( Brown wire). I have seen plate brackets with built in lights or lights by themselves.
My opinion there is plenty of red LED light when the running lights are on but check your local State or provincial laws regarding trailer license