Flickering or pulstating Headlights

Redfish and 67dart273 may have something more to suggest.
What I see is not only some flickering, but high voltage. 14.5 to almost 16 V.
For ref it would be useful to know what alternator, what regulator, and how you rewired the alternator and battery feeds to the main splice.

Now that you have a new battery I think the next steps are:
a) Start the engine and measure the voltage
1. as close as you can to the regulator 'sensing' terminal.*
2. at the alternator output.
3. between the two because its easier to see the difference when measured directly.

b) Put an electric load on the system and repeat measurements. (For a load, turn the headlights and/or heater fan.)

*The easist places to measure the voltage the regulator is sensing will probably be at the alternator and at the ballast resistor.
Schematically a 70 alternator circuit is wired like this:
upload_2019-4-21_9-32-50.png
(insulation colors and terminal positions are representative and vary from year and model)

Voltage measured at any of these points to ground should be the same.
Voltage measured between any of these points should be close to zero.
upload_2019-4-21_9-45-28.png