Meaningless explanation:
I am a full time Hunter, part time Gunslinger. I thoroughly enjoy the satisfaction provided by the Golden Gun, whether it be stopping a stormtranced warlock or a sunbreaking titan, or destroying a major enemy with a resounding blast. It is a reliable damage dealer. That being said, (mostly in pvp but occasionally in pve) I can get the immediate kill, but then have to rush around frantically to find another target, lest I waste the crucial 1-2 powerful shots.
Actual suggestion:
Change a perk to grant extended golden gun time for the first kill or all kills with the golden gun. While not being a universal boost to the amount of time, this would be based on your aim and situation, making it not too OP as a universal buff. This could give more time to find other targets, and not be forced to rush headlong into what could be a fatal confrontation due to said rushed approach. Other supers share similar perks, so it is not unheard of. This may be a terrible idea, but I hope it could at least be considered.
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In PvE you are not obligated to use all three shots. Your hunters life is not forfeit should you only use one or two shots. That is not how it works. It's for generating orbs for other players, or helping you out in a tough situation. I would agree to a very slight time boost per precision kill though. Reward hunters for actually being precise.