I want to add light clusters (indicators, rear lights and stop lights) to my bike trailer, which can be controlled from my bike.
No, the kind they have at the automotive store are the best bet. You don't want the lights on your trailer to fail going down the road. You want that hard wired, not relying on some bluetooth module that may or may not last.
If you're talking about the indicator lights like the brakes and the turn signals, then there really is no place for an Arduino in that. The Arduino simply isn't needed. All of that stuff just uses basic switches and things. There's not a job there for the Arduino to do. Not if you're staying legal anyway.