Fire duration is case-specific, thus it's one of the many details left to the user's discretion, based on their assessment and tolerance of risks. Similarly, you'll notice that codes and standards don't define what causes the pool fire (what burns). Aside from storage tanks located in the US (OSHA 1910.106 regulation), the user is responsible for assess whether the relief device needs to be sized for fire exposure. In some cases it may be reasonable to conclude that the fuel will be consumed before the surrounding vessels are overpressured.
For your specific case, my attention is drawn to the size of the vessel (1 gal), more so than the possibility that the fire will extinguish itself. Does this 1 gal vessel justify a fire sized relief valve? In my opinion, the answer is generally no. The high surface-to-volume ratio means that the heat flux is high. The liquid is going to be gone in very short period of time (probably less than a minute). So, after installing a fire-sized PRV, have you really accomplished much with regard to risk reduction? Again, my answer is no. Once this vessel is empty of liquid, it's going to quickly heat up and fail due to high temperature - the PRV isn't providing any real protection from fire exposure once all the liquid has vaporized. So, this vessel is probably going to fail pretty quickly, regardless of whether you've sized the PSV for fire exposure or not. There are exceptions, but for most cases like this I see little to no value in sizing the PRV for fire, and that's a judgment decision the user can make.