The stud/nut clamps the manifold to the cylinder head on the right side of the exhaust port so if there's nothing clamping it down, it will leak exhaust gasses and tick.
Check your other bolts/nuts on the exhaust manifolds and make sure none are loose or fill a spray bottle with soapy water. Spray the solution over the manifolds and look for bubbles. If bubbles appear, you've found the leak(s).
Inspection cover - You won't break it unless you're real rough w/it. Take a small flat blade screwdriver and pry out the inspection cover, shine a flashlight to look for any cracks. You'll need to rotate the engine over by hand (ratchet and socket on the crank bolt) so you can see the entirety of the flex plate.
If it's the flex plate (and I'm hoping it's not because I'll look like a complete dumbass;
@wjburken will look genius and good on him for calling it), you'll need to yank the trans and replace it. Buy new torque converter and flex plate-to-crank bolts.
If the sound is coming from the transmission itself, the only things I can think of that would cause it are the pump (could be but not likely - when these start whining or making noise, they fail very shortly thereafter the noise first appears) or the pinion gear needle bearings in one or both planetary carrier assemblies (more likely this than the pump but still not high on my list of suspects). If it was converter, you'd likely know it as there'd be unmistakable drivability symptoms (shuddering, loss of power, 'grinding' or 'galling' type noises) then converter failure shortly thereafter.
FWIW, unless the sound in the vid in your earlier post is not representative of what you're actually hearing in person, it sounds identical to the ticking sound my Tahoe makes and like I said earlier, it's been nothing more than a mild annoyance at worst in the past 10 years (that stud in the above pic has been broken since I bought the truck in 2013).
