I have a 2003 chevy cavalier. Recently a “clicking” noise originated from underneath my dashboard. It happens only when the car is running and it consistently happens. It sounds like something is hitting the fan over and over again. I just wanted some info on what my problem is. Thanks.
Is something hitting the fan over and over again? 
Is your fan on when the noise is happening? What happens when you turn the fan off? What about the radio? What kind of clicking? Does it sound like the turn signal? Snapping fingers? What’s the frequency of the clicking? Where under the dashboard? Passenger side? Driver? Middle?
If the clicking changes speed with the fan (heater/a-c) speed, then it’s probably a leaf that’s caught in the fan. I got rid of mine by running it at max speed for a little while.
The noise is constant when the engine is on. It doesn’t matter if the fan is on or off. The clicking is loud enough to where I can drive 70mph, have the radio on medium volume and still here it. I would say the noise does sound like some turn signals. The sound sounds like it is coming from behind my climate controls under the center part of the dash.
What happens if you turn the key to “on” without actually starting the engine?
No noise
A relay maybe?
If it was the fan, agree the clicking should change with fan speed, but also if the engine is off and the accessories on, the fan can still be on.