When I turn on the headlights, running lights too, during the day, the dash lights dim to the degree that the displays (radio,etc.) can not be read.
Is that an issue just with my fj, or a general engineering flaw?
Its not an issue or an engineering flaw.
Its designed to dim when to turn your lights on.
You can increase the brightness of your dash lights using the rotary switch next to your steering wheel, but I am not sure if that will brighten your radio ...
That was normal on my Carola till after dark, then dash lights came on like with my 13 FJ, so i just considered it normal. With the Carola there was a little light sensor on the dash that if i covered it the dash lights would brighten.