In the Utility business we would suspect a loose neutral wire or bad ground in the Main Service Panel
That translates to: You probably have a bad ground in you light circuit. Are we talking about the intrument panel? If so, There is a common ground point up under the dash you may need to check to make sure it is clean and grounded tightly.
Chances are if the head lights don't dim when getting off the gas and the interior lights eg.. overhead and walk a round light are ok then it is likely to be common to the one circuit.. It doesn't hurt anything to check all the ground points every so often either.
The ground connection point is located on the side panel up under the drivers side to the cage frame via a bolt... I think it is a 7/16" bolt head.. Not sure about that.. This is the main ground point for the intrument cluster.. Be sure to check connections at the Lights too.. maybe be a loose connection on the HOT leg too.