I took out the drivers side headlight assembly and checked my turn signal bulb. It was in good shape. I took the advice of this forum and made sure the connection points for that bulb were clean and I slightly bent them in toward where they meet the bulb. Essentially making it a much tighter seat for the bulb.

This seems to have solved my problem.

 

Got a 2004 ram 1500.. just replaced the headlight assembly and now my lamp out light flashes and the console dings while the directionals are on... while the directional is on it will ding for 10 seconds stop and then start back up...

 

During a period of fairly wet weather here, my lamp out alert returned. Coming on and going off several times a minute for long drives. Very frustrating since I thought my problem had been previously solved.

Turns out, it was simpler to fix this time. My left brake light failed. It would work as a running light when I had the lights on, but pressing the brake pedal, it would not brighten. I replaced the half working bulb and presto! The problem was solved. Very strange that it initially had the same symptoms as I had had before....maybe my experience will help somebody out in the future.