When it is acting up remove power to the circuit and check for shorts betweeen all the wires one pair at a time at the connector with an ohmmeter. You can also leave power on and check for voltage from each wire to ground. During normal operation only pin 4 should be always hot. All other pins should only be hot when active i.e. only pin 6, right turn signal, and pin 4, always hot, should be hot when you turn on the right turn signal. BTW, the right turn signal and right brake light are on the same pin. This could be related to the warning conditons you last posted. The 7 pin diagram on this site should help. http://www.etrailer.com/faq-wiring.aspx
My first thought is the problem is either internal to the rear connector or the connector that I expect you'll find at the firewall. Not sure about the new RAM, but my Ford van had a connector right under the firewall between the engine bay harness and the body harness. If I was the dealer I would have replaced the rear connector out of hand the first time you brought it in. Hope this helps.