I have been trying to complete the quest for the Last Word for the last 28 deaths and I wanted to reported that no matter when you shoot the gun out of Enkaar's hand 9 deaths out of 10 he still manages to shoot you even when he's pointing his gun away from you. The only way to get past him is to shoot him in the split second his draw animation start. Now that works on the first stage but on stage two you can never move the stick fast enough to shoot the second one.
I watched a couple of videos on how to do it and I noticed that all of those players have a second or more to aim and shoot after the start of the drawing animation.
And no, it's not lag, the latency is in the low tens of milliseconds.
Update 23 June: after today's server reset I tried the quest again and I managed to complete it without weird deaths and a lack of spawning in the 2nd stage.
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Pretty sure you have to hip fire at their guns in the order they spawn. If you aim and fire i believe it auto fails