The repeated "Recover!" is indeed the formation leader, not an automated warning. It's as regular as it is because pilots, and especially military pilots, are trained to maintain a very strong radio discipline, and also (as Brian Shul notes in Sled Driver, his SR-71 memoir) because as a point of personal and cultural pride everyone wants to sound like Chuck Yeager on the radio. It makes sense, too; things can go wrong very fast in an airplane, and it does no one any good for a pilot to lose their cool in an emergency.

Listen closely, and you'll notice that the formation leader lets that discipline fray a bit in the second and following calls, when some urgency bleeds through. This is because he suspects his trainee is about to die, which is what would indeed have happened if AGCAS hadn't been available.

(You can also tell it's a radio call and not an annunciator by the form of address - the full call is "Two, recover!"; "Two" is what someone else in the formation calls its second member. "One" is the formation leader; in a four-ship formation you'd also have "Three" and "Four", and so on for larger groups.)

edit: corrected some terminology

> Listen closely, and you'll notice that the element leader lets that discipline fray a bit

Actually, the moment I heard him, I thought there was terror/panic in his voice which is warranted because

> because he suspects his trainee is about to die

came very close. Went from over 16,000 ft to under 5,000 ft.

One thing I did not think was "this is a machine talking".

Yep. The actual AGCAS annunciation is the pair of chevrons advancing from the sides of the HUD into the center, and the blinking cross and "FLYUP" indicates that the system has engaged.

For audio, there's a very noticeable horn during recovery, as well as a "Fly up" automatic voice announcement - that's a little hard to pick up due to overlap with a call from the formation leader, but you can catch it if you listen closely.

There's also an automated (and very calm) voice announcement saying "altitude" 2-3 times before the urgent "fly up!" and horn.

I guessed that he probably suspected he's unconscious or something, and therefore warranted shouting.

After all, the leader had probably seen Top Gun, where this almost happened to Cougar :)

Well yeah, formal radio comms have to be. It's not like Top Gun.