[JayChicago]

Theoretical guess here:

Original post said: "when I put on brakes the dash lights go dim and headlights get even weaker". That makes me think that when brake lights go on the entire ground bus (the body of the car) is being charged, reducing its ability to take-on ground voltage from the other lights. So why is the ground bus not immediately discharging to the battery as it should?

I would suggest cleaning/tightening the battery-to-body cable connections.