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It would have to be placed in parallel with the light output to do anything. Standard capacitors are spectacularly un-energy-dense so you'd want a super-capacitor for it to last more than a few seconds.
That's pretty much all the standlight in a basic rear light is, except there are usually some diodes and resistors and things to regulate the charging voltage and slow down the discharge current a bit.
So, the wires are correct (because #hippyisalwaysright) and if they are reversed the rear light doesn't work at all. I guess that points to the cap being a bit shit in the headlight. Any other brilliant (your a lumen!) ideas?