Blade Runner

I think with Zhora, Deckard was able to track her possible location through the snake scale and that photograph... but he's basically still following promising leads rather than absolute facts.

Deckard is basically doing recon on Zhora because the photofit he had wasn't great, but his cover is blown and she turned violent.
As it happened, the fact his cover was blown and she turned violent is also the very reason he was able to confirm she is the one he is after.
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Remember the photo of Zhora... she was wearing a headpiece, meaning he doesn't know exactly what she looks like.
When he goes to the club, he talks to Zhora, checking her out to see if she is the one he's after... she gets suspicious though and attacks him and then flees.
She also only flees because people walked into the room when she had Deckard dead to rights. He only survived the attack by sheer luck.
It's only now, when he's absolutely sure that she's the Replicant he's after, that he actually shoots her.

The problem with hunting a rogue malfunctioning Replicant... that doesn't want to be found... is that if you go in guns drawn, they'll immediately attack and probably kill you.
The other problem, going in guns drawn and opening fire... you could well kill an innocent. Or worse, a real person.
The example of this is Pris and Leon. The moment they see Deckard, knowing he's there to hunt and kill them... what do they do? They attack. Immediately. Without question they simply try to kill him on site.
If Zhora knew Deckard was a Blade Runner, she would probably attack him straight away... but he goes in as a Union Officer (or whatever) and she's cordial with him. But, once his cover is blown... she goes into kill mode.

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