Sorry for the late response, was at Disneyland for a few days.
Not sure if it's the same issue or not, but I had a problem where my left turn signal would not function if the engine was running. Turned out to be a faulty speedo that was shorting the turn signal when the headlight or speedo were lit up (read: whenever the engine was running).
If checking your connectors doesn't fix it, you might want to have your dealer check into the integrity of the speedo as well.
Good luck!