Might be nothing to do with it, but is the trailer cable itself ok ? I had an IW sheep trailer a while back that had problems with the lights, one indicator was working intermittently (not in the usual way !). All the socket connections and bulbs checked out ok so I put new cable on and it cured it.
This may well be the answer. Might order a new lead and plug, the current one is looking a bit worse for wear but I can't see any breaks. But that's not to say it isn't.