There is the possibility of a bad sensor on your gas tank, bit I am telling you that it will be cheaper to got to a shop and have the smoke test done. My 04 V6 has the same problem. I have been researching and hunting and the cheapest way is a smoke test. If you have a chain close to you, like Tires Plus, Raffield Tire Master, Firestone, or even a Sears, they should have the before mentioned smoke machine. To replace the sensor is not easy nor cheap. I do not know what the clicking could be.
Mobile device via Mustang Evolution app....