One of my rear side lights stays out, unless I use the turn signal, then it works fine. I switched bulbs with the other side and the bulb works fine on the good side, so it's a wiring or switch problem, right?
It sounds like it could be either a ground problem at the light or a bad connection in the socket itself. Have you looked at the contacts where the bulb make connection?
The rear lights are single filaments and that is where there may be a problem. They should not be on with the ignition. Is the other side lit then you turn on the ignition? If it is you may have the wrong bulb in it. There should be one contact on the base unlike the fronts that have two.
Also do you have any load equalizers in the system?