94 Honda Accord Headlight Problem

We have a 94 Honda Accord (154K mi, V-Tec 4 cyl. Eng.) That is recently giving us fits with the headlights. Once we turn on the car and then turnon the headlights, the headlights blink rythmically 3 times and then shut off. Once the headlights shut off, the high beams also do not work. Every time we retry turning on the headlights, we get the same result (whether the car is on or off).

All other lights work fine, however (brake lights, turn lights, int. Lights, etc.)

The battery is fine (12V), and the alternator charge fine (14.5 amps).

How can I find out what is causing this problem?