THe CVR will affect the gauges. It sounds like when the alt gets up to speed and starts pushing a charge to the battery-meaning the current flow increases to something more than a small trickle ( at idle) that a gound connection is breaking down somewhere. WHat is the voltage output from the alt above 1k rpm? SHould be around 14v or so. Curious to know if that measurement is a lot higher than 15v...
THere is a ground wire that should be attached behind the inst cluster, if that is off, it might cause a problem. If the gauges work then it's probably attached...
If its ALL the lights, including tail lights, headlights, parking lights, etc, then I would also lean toward the voltage regulater, and/or the alt. I've (rarely) seen a failed regulater take out the alt and vs versa and you chase the two parts around untill you replace both at the same time...have you have a parts stor spin the alt to check it out yet? New does not mean good...
Will be intersting to see what fixes this.