In this MD-11 stall test video, are we seeing the tail stalling first?
The entire tail is shaking (not just the horizontal stabilizer) not because it's stalling but because it is in the turbulent wake of the main wing.  The tail is generating downforce as you can see from the up elevator.  The main wing's nose down pitching moment increases when the center of pressure shifts aft at stall, as well as the change in the overall center of lift outboard and aft due to wing sweep as the root stalls with the outer end still flying.
The increase in pitching moment exceeds the downforce that the tail is able to produce, and the wing wins the force balance tug-of-war with the tail, and the airplane pitches over.
If the tail itself stalled, the nose would pitch over radically from the near complete removal of downforce, as if the pilot suddenly shoved the stick forward. That's not what is happening in the video.  When this happens the tail's local AOA can increase further due to the pitch over and and a partially stalled tail can stall completely as if you sawed it off, and the airplane ends up pointed at the ground, as demonstrated in this testing in a Twin Otter.
I recall another incident in in a Twin Otter in the Canadian Arctic where tail stall was induced by the pilot pitching over hard after a zoom climb right after takeoff.  Extreme pitch rotation at low speed means very high local AOA at the tail's leading edge. The pitch over rotation cause the horizontal tail's stall AOA to be exceeded when the pilot re-applied up elevator, and once exceeded it just got worse, and the Twin Otter just pitched over straight into the ground.