First of all, what kind of stereo system do you have? If you have a big one, it will pull from the system causing the lights to dance.
What condition is your battery cables in, and your ground strap? I replaced my factory ones with heavy gauge sealed end cables. And I use those felt washers and anti corrosion spray on my battery terminals. It keeps corrosion away. And when I installed my motor 6 years ago, I put in new ground wires on the exhaust side, valve cover to firewall, and neg post to fender. And made sure I roughed up the area to get a good contact.
Another thing, with the engine running, take a volt ohm meter and test the amount of voltage it flowing through the battery. A normal good system should be 13.5 to 14.2 volts. (around there) After you have that baseline, now turn on headlights, heater, wipers, and stereo system, and see what the volts are. If it really doesn't change then the issue might be a battery, but if it does, you might need to look at your alt. But you need to have a good strong battery too. So, make sure your battery is in really good condition before assuming your alt it the culprit.
After that, turn everything off including motor. See what your volts is reading. The volts should hold steady without dropping.
And how old is your battery? If you don't know use this chart. On all batteries there will be a round sticker with a letter / number.
A -- Jan
B -- Feb
C -- March
D -- April
E -- May
F -- June
G -- July
H -- Aug
I -- Sept
J -- Oct
K -- Nov
L -- Dec
And the number represents the last digit of the year it was made. So if you see F/9. It was made in June 2009.
After re-reading your post, another question is, do they pulse when you have your blinkers on? My alt gauge flickers a little too, when I have my blinkers on, only because they share the same ground. But my headlights don't flicker. Just the gauge.