Flickering or pulstating Headlights

Or maybe a new ignition switch would fix it? Of course the relay would probably be a lot cheaper. Does the relay fix the fluctuating voltage at the battery too?
Yes it does. The reason the lights are flickering is because the voltage is fluctuating. The reason the voltage is fluctuating is because the voltage from the ignition switch and going to the center (I) terminal on the regulator is fluctuating due to the dirty or worn ignition switch contacts. The I terminal is how the regulator senses how much charge is needed. It drove me nuts until I came up with this fix. Trust me it will fix it and it's probably an under $10.00 fix. Let me know if I can help.