The guy in that video is overthinking it slightly, but that's not a terrible DIY method to figure it out.
If it was me, I just set the blower speed to low, then turn the temp knob slowly through it's full range. If the knock/pop show up doing that, it's the temp door actuator. If not, I move over to the mode knob.
On the mode knob, make sure to start in defrost, and work slowly through the settings. If it starts popping/knocking, make sure the LED on the recirculation button didn't illuminate. If it did, stop, and press the recirculation button to see if it pops or knocks again. If the recirculation button doesn't cause the noise to reappear, it's the mode door actuator. If it does, it's the recirculation door actuator. The video posted by
@acutron42 shows where all three are, the guy in the video just doesn't name them by name.
They're relatively cheap, even at the dealership, and easy to install.
You get less help in the S197 section of any given Mustang forum because far fewer S197 owners are DIYers. When I bought my 2010 GT in 2010, I was shocked and appalled to find that 90% of the discussion was about cosmetic bull
and which shops and dealerships they had working on their cars. It was a big culture shock coming from the Mustang II and fox-body sections. It has changed quite a bit over time, as the cars age and find their 2nd and 3rd owners, but it hasn't gotten to the point of their being nearly as DIY-involved as previous generations. Part of that is because these cars are so damned reliable, (except for my 2009 GT/CS, but that's another story), part of it is because they're considerably more complicated than the generations before them.