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Does anybodies headlights dim and the a/c fan speed go lower when they hit the brakes?
Not much, but some. Consider: your foot is off the accelerator, so the engine drops to idle RPM (which reduces the maximum alternator output by a bit). Now, if your lights are all on and your A/C (and possibly other accessories like a custom sound system are all pulling current), the extra draw caused by the increased current demand to the brake lights might just reduce the voltage enough for you to notice as reduced light output and a slower A/C fan.
Alternators try to keep the voltage constant over the RPM envelope, which is why they've replaced generators, but they can't work miracles. Still, if you have a BIG drop at idle, it could indicate a weak charging system.