89 Jeep Cherokee Lareodo electrical problem

Suddenly the other night, after having replaced the battery cables, a wierd electrical problem started happening. All the lights will dim then brite, then dim....the voltmeter will erratically show power going from 9V to 14V and back and forth.......any clues on what is doing this? the battery is new and full charged, the altenator is brand new, new battery cables........

My first thought would be the voltage regulator.