Chris, the door will be at the exit from the exhaust fan housing, where the round ductwork begins. You'll have to remove the vent/light cover, and then the fan itself to get to it. Fan removal is usually very easy; the fan unplugs (visible inside once the cover is removed), and often "snaps" into place with tabs, or one or two screws, and the fan will be free to come out.
Actually, there's not really anything you could do to the door to solve the problem, so I'd probably just use a stepstool so I could listen at the vent to see if the "ticking" became familiar as the sound of a little plastic door tapping as it moved. The only possible way to end the ticking would be to try a different style exhaust cover outside, which might help prevent draft moving the door.
If nothing else, and the door is making the noise, you'll feel better knowing what it is.