I was having the same problem, pulsing lights, CD player would lose power. I added a battery negative to chassis ground and a block (intake manifold bolt) to chassis ground and the problem went away...
It sounds like a bad alternator or voltage regulator. Mine did the same thing for a short before the alternator failed. I replaced both the alt and voltage regulator and the problem was fixed. I especially noticed it at night with dash/interior lights, etc.