Constant flasher clicking sound.

have you had someone stand in front and the back of the car while you switch all lights INDIVIDUALLY on and off ? do they all work properly ?
check to make sure there are no loose connections/corroded connections .
there is also a control module (probably called differently) that may simply have started to malfunction .
having the problem dignosed and repaired by an automotive electrician would probably be the quickest fix .
if you want to do a "self-diagnosis" you may be able to find a manual for your car at your local library or at an automotive supply store .
hbg