Im an electrical engineer I hope I dont talk over your head ill try not to.
Your dash lights along with headlights, and other exteror lights and some times interior lights all form one potetial path. Yes some are grounded seperatly but some are grounded the same place. Most of your exterior lights and illumination light all come from the same potential source. Such as a fuse, or series of fuses that come from the same sorce.
When your engine is turning at say 2500 RPM the alternator generates a certain voltage. Say 13.7 volts. When you are coming to a stop you push in the clutch and press the brake pedal. The engine now turns 600 RPMs. The output of the alternator is say 13.1 volts. But more so is maxed for current output do to the lower velocity. So if you have a larger current consumption from all your electrical components. You may or may not be peaking this output.
Now the two instances combined. All your power comes from the same fuse or wire for your lights. With age, combined with corrosion and body rust, your complete lighting circuit has a particular resistance in it. The aged resistance is much more then when the car was new. When pressing the break pedal you turn on your brake light bulbs. These bulbs are inheartly the highest draw bulbs in your car besides your headlights. They are parrallel with the rest of your lighting causing a higher draw of current. This higher draw, runs threw the resistance i previously discused causing a larger voltage drop then without the brake lights on. This voltage drop may be only 1 or 2 volts. But combine that with the slowed alternator speed and there should be enough voltage diffrence to show a dimming of the lights.
I do not know how significat this drop is on your car but all cars do it to a minute extent. If your battery and alternator are in perfect condition. You may want to check and clean corrosion at the battery terminals. Where the neg cable grounds to the chasis, and both ends of the ground from the engine to the chasis. Ill bet that at one of these location there is some extra corrosion. Posibly in the bulb sockets as well, but wont make as much of a problem as the main points i mentioned.
Hope i didnt bore or confuse you
