1994 Hyundai Pony Electrity goes on and off, engine stall

I have had the following problem 3 times in the last 2 weeks: when the engine is running idle, at some point all the electric parts (radio, clock, mirror and dashboard lamps etc.), start going on and off quickly (flickering) for 4 or 5 seconds, and then the engine stalls. If I try to restart the car, it sounds like the battery is completely dead, but after waiting a couple of minutes, the engine starts just fine. I've tested both battery and alternator and they seem fine (12,4V on the battery, 14V on the alternator). What could be the problem?