Trailer lights have me baffled?????

Almost invariably when the exterior lights start acting up it's a grounding problem. Usually the lights gain a ground through a different lights. This can cause weird behavior like when yuo step on the brakes one taillight goes out.

But, I would first check though that the lights have the correct bulbs in them. Pull the bulbs and look in the sockets. If the socket has two contacts, make sure the bulb base has two contacts.