LED turn signals

I recently intsalled a set of LED taillights on my mom's 98 corvette. the LED turn signals are complete housings and designed to work at 14.4V and are supposed to provide enough resistance to keep the GM turn signal bulb indicator from double flashing. (the GM system causes the turn signals to double flash if there's drop in current through the turn signal bulb)

the LED system normally works fine except when the car is braking. apparently the voltage level drops which causes the signals to double flash. i've been told this is cause the engine bogs down and slows the alternator. i have a theroy that this could be solved with the use of a small capacitor to store up power then release it during those few seconds when the voltage drops.

what type/grade/rating of capacitor should i be looking for?

Leds arent going to create enough of a load to cause your alternator to struggle .  Take a multi meter and measure the current going through one of the led tail lights with just the blinker and then measure blinker and brake and come back with the numbas.  Measure voltage as well just in case.