There is no electric lock for the fuel cap. The only electric lock is the one on the trunk latch controlled by the PTCM. WHERE is the sound coming from?
Here is how it all works:
Fob talks to SKREEM which tells the Body Control Module which tells the CLP/SSM to lock or unlock.
or...
Button on console tells the Body Control MOdule which tells the CLP/SSM to lock or unlock.

The turn signals are flashed by the SKREEM when you use the FOB.

If there is a CAN BUS failure between the BCM and CLP/SSM, I can see it manifesting in the way your car acts. But almost EVERY time, it's the damn CLP/SSM.