Head lights dims down when letting go off the gas or stepping on the breaks

When I'm driving and I let go the gas to then break or decelerate, my head lights dims down. If my CD player is also running at the same time, It stops the music for a full second. The vehicle also seems to be very quiet for that full second, like everything is going to shut down. (Scary on the high way!) A couple of times the car kind of coughed and jerked. I also have a hissing sound from the speakers. Especially when I hit the 4 window up button when they are already up.

What I checked so far: Battery voltage: 12.55V, running: 14V at start up, 13.55V after a ride, Full load seems to be fine! I've checked if I'm loosing voltage from the alternator (positive of voltmeter on battery negative, negative of voltmeter on alternator casing) Checked ground straps battery to chassis, chassis to motor. I just saw the AC test for the alternator, to see if a diode failed.I'll do that in a couple of minutes?

Could it be the break switch? Very strange, but the problem seems to be less apparent when it's raining outside? Any other test to know if I'm loosing negative/ground somewhere?