2003 ram 2500 4X4 5.7. When the headlights are on and I turn on the right or left turn signal, the lamp out light comes on as well as the chime. ALL lights are working both front and rear turn signals flash when activated. When the headlights are off and I activate the left or right turn signal the lamp out light does NOT come on nor the chime. Anyone had this issue? The turn signals work fine but when the headlights are on the lamp out light comes on and the chime. The chime is annoying.

 

Yes. Can be annoying. Took me a couple months to finally find a burnt contact wire in one on the signal bulbs. I believe i posted a pic. Do a search on here. Believe its been discussed many times. First thoughts sound like you have a ground issue. The ground can handle either headlights or signals but not both at the same time. Start checking your grounds.