My Series 2 ignition light was pulsing about once every two seconds and the headlights were visibly dimming and brightening at the same time. The pulsing was not dependent on rpm. The charge voltage was good. The voltage regulator was working properly.
I suspected a voltage drop between the alternator and the voltage regulator +ve terminal.
So I connected a wire between the alternator output and the + terminal on the voltage regulator. The pulsing stopped.
Looking at where this voltage drop could occur, I decided to look at the alternator’s relay contacts and wire connectors. I took out the relay, cleaned the contacts and its spade terminals. Then I tightened the female push-on connectors by squeezing them with pliers so they were harder to push onto the relay spade connectors
Problem fixed. Hopes this is useful to someone in the future!