the small alternator doesnt sound like its the problem. The battery doesnt drop to zero then get suddenly recharged by the alt, there is always a surplus of energy. Want an easy way to check, spend 5 mins, remove your alternator belt, start the car flick the ac on off and do whatever else causes it to flicker. It will still do it I bet. Batt usually last me 5-15 mins of normal driving without and alternator before it gets fully drained so dont go for more then a few minutes cruise, have the car already warmed up before removing the belt since it may not do the flicker during warmup for some reason. Make sure you dont fully drain your batt as this will damage it.