Maybe a small lead-acid, gel-cell battery? Obviously not cheap, but... Keep it trickle charged from a 12V line through a resistor. It's possible NiMH batteries could supply 8 amps, you'll have to look it up. Certainly the ones from RC cars and planes should. Since this is a case where you need large currents for a small period, a battery like this might work.
Maybe even a stupidly-large capacitor, but not sure they'd have the energy capacity.
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-------------------------------------------------------------------------------- "There's nothing like eating hay when you're faint," the White King remarked to Alice, as he munched away. "I should think throwing cold water over you would be better," Alice suggested: "--or some sal-volatile." "I didn't say there was nothing better," the King replied. "I said there was nothing like it." Which Alice did not venture to deny.