why are my electronics in my 2006 ford five hundred diming and going bright again when i press the throttle

Noticing lights and electronic readings in your vehicle get brighter and dimmer with acceleration and deceleration seems to be an example of a charging system that may not be providing enough electrical power to recharge the battery consistently and maintain proper reference voltage in vehicle operation. I would recommend having the charging system checked, along with the battery to make sure everything is running as it should. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops