First thing to note, is that all lights must meet ADR requirements. This is either by being listed on the RVCS, or being stamped with ECE compliance. That means no cheap-arsed ebay knockoffs..
Rear position Lamps (tail lamps), 2 lamps. Must operated with towing vehicle tail lamps.
Rear stop lamps (Brake lights), 2 lamps. Must operate with towing vehicle stop lamps
Direction Indicator Lamps (Turn Signals), 2 lamps.. Must operate with towing vehicle indicator lamps.
Rear registration lamp, at least 1 (Some lamps may only be approved if fitted in pairs). Must operate with towing vehicle tail lamps.
Side marking lamps, arrangement at the side, one lamp each side within the first third and/or one within the last third. (aka in the first or last third of the length. Since the drawbar will be long on a bike trailer, I’d have it within the last third). Note, that these are ONLY required on trailers more than 6 meters long. However as anyone who has towed at night knows, side marker lamps are the only way to know where your trailer is! So I ALWAYS have them on a trailer… There is no specific requirement for how these are electrically connected. I’ll have them on with the tail lights..