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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Honestly, i think that the gunslinger class is fine as it is, the perfect balance of power and vulnerability. I think the time frame really puts you in a position where you have to think about how to best use your special.