Pulsing headlights and dash lights

Hundreds of posts with extensive diagnostic procedures will be found in this forum.
If you wish to go that route first, have fun. I'll only say that the condition you described is most likely a failed voltage regulator and it wont break your bank or your back to throw that one part at the problem.
A couple years ago I tore into my 67 and added later model charging system, electronic ignition, headlight relays, amp gauge to volts gauge conversion, etc,, etc..
The very next day a pulse in the volts gauge identical to what you have described appeared.
Since many of the components I installed were taken from a 73 model donor car I had to bet that voltage regulator had failed. I won that bet. Not one electrical issue since but I had already been the back breaking route in doing those upgrades that I merely wanted, not needed.