Pulsing headlights and dash lights

I have a 1966 Barracuda that has recently developed an annoying problem. When turning on the headlights, both the headlights and dash lights have a steady pulse to them going from brighter to dimmer. It is not something that happens only when I stop and then steadies upon acceleration, it has nothing to do with engine rpm and does not pulse faster and slower with engine speed but is at a very steady rate. Has anyone else had this problem and what is the solution? My initial thoughts are electronic voltage regulator and/or upgrading to a 60 amp alternator. Relays, but where do they wire in?
Any help is appreciated. Thanks.