Clicking in the dash board?

Shortly after I purchased my used 2003 impala (3.8) with 45,000 miles on it, the 'Security Light' would come on 80% of the time once I got up to 2 rpms. When the light would come on, I could hear a clicking sound on the passenger side of the dash board, in the evenings I would notice that my headlights would flash along with this clicking. I had in in to two different repair shops and neither could find an answer and the clicking and flashing would only occur for a very short time -- it would click up to a dozen times. Now, the clicking does not stop and I am noticing the lights flickering in too. When I come to a stop sign or slow down, then it is fine. It is just when it is above 2 rpms.

Any advice for me? I am super frustrated and know very little about cars.