My 99 Maxima has started making a high pitched sound that alternates on and off along with the normal turn signal sound. It varies in pitch and in some cases it will fade if the signal is on long enough. It happens on both left and right signal. It's driving me crazy because to most people its barely noticeable but I can even hear it when the stereos up.

 

This might be caused by a sympathetic vibration in a part near the flasher. Perhaps you can find it by feeling around under the dash in the vicinity of the flasher. Grope until you touch something which makes the unwanted sound go away. Then eliminate the sound permanently by pushing the vibrating part to a different position or wrapping it in a sound-absorbent material such as foam rubber.