My 2005 Crossfire roadster basic has what sounds like a relay static noise. coming from just behind top of firewall under center of dash. The noise used to go away after starting car, but now continues even after starting. Car seems to start and run Ok, I originally thought it sounded like it was coming from the RCM module and replaced it,and found what looked like burn marks on the large fuse and replaced it. That appeared to fix it but a few days later it came right back now sounding from the under the dash location. Any ideas? Thanks!

 

I am just guessing from what I have read, but maybe it's the alarm-siren? The siren is located under the wind shield wiper cowl in the center of the car. If it is the original your batteries might be leaking. When they go bad and leak it causes problems on the circuit board.
There are many posts on this. Just type "Alarm" into the "Search Threads" box in the upper right.
Hopefully one of the senior members will see your post and have a better answer for you. Good luck!

 

Also, have you replaced the cabin filter under the glove box? If it is dirty with leaves and twigs the fan can make noise.