The book only mentions the procedure for starting at the gate with APU inop. It does not mention how the shutdown procedure would go in that specific situation.

There's only 2 points that I could find that are relevant:

1. Single engine taxi with APU inop is prohibited
2. 2 minute cool down is required before engine shutdown

I would not call pulling into the gate with both engines running while waiting for GPU and/or cool down "normal", due to common sense hopefully, but the book does not specifically forbid us from doing so.

Short taxi? Also, aren’t ground crew trained not to approach the aircraft with the beacon on when pulling into the gate? I think you’re reaching for ideas to blame the flight crew.

I'm former ramp for the other WO AA carrier. That might be on some LMS slide in training, but in practice as soon as the plane comes to a complete stop everybody tries to chock the tires and start unloading. We would have had no real way of knowing whether the APU was deferred or not. In my experience, it's usually not particularly hard to notice if an engine is still running but when I started I made the mistake of walking around the back of a 175 when an engine was idling (whether the APU was deferred or not, I'll never know) and got blown across the ramp

There is pressure to go, go, go on everyone's part. Sometimes we all just go too fast. I know it's hard, but sometimes we just need to take a deep breath before we act. This guy paid the ultimate price. Too bad.

Single engine tacit with apu inop being prohibited would result in arriving at the gate with both running.

Yes, if the beacon was on (I'm assuming it was) then this is a colossal failure of fundamental safety on the part of the ramp. Remotely possible that the lower beacon failed or the CA reverted to muscle memory and turned the beacon off. We'll know soon enough.

There are things we can do to minimize risk, good practice to slow-roll a short taxi-in to avoid having to finish cooling down while parked at the gate. Worst case stop short of the parked position and then pull in after cooldown.

With APU inop, you just have to keep one of them running though so that's where the adherence to procedure becomes absolutely vital... it's not an uncommon occurrence. Might be worth advising ops which engine will remain up, but they still should just stay the eff away except for the guy who has to plug in the power and maybe nose chocks.

I vaguely recall shutting down #1 on a past airplane because the GP receptacle was on the left side. Might have been a prop job.

Flashing red beacon would be on any time an engine is running. That’s how you would know not to approach.

Right, as a pilot, that may be intuitive. As a ramper with 5 days of training you don't/barely know what a beacon light is, much less what it represents. The standing practice in a lot of places is you listen for the sound of the engine being cut

That's what the beacon is for.

Unless he was wearing his airpods.