No bright lights - 2001 Ford Explorer Sport

check for a loose dirty earth point for the lights. wire not earthed to a pint that is connected back to the battery.

check the bulb sockets , ck your ground

Ground problem with the light wireing .

Your circuit lights may be bright or dim according to how your electrical system was set up. It may dim when lights are off and get bright when lights are on. ------------------------------------------------------------------------------------------
Car Diagnostic Tools

DOME LIGHT STAYING ON BECAUSE YOU HAVE BAD DOOR SWITCH OR BRIGHTNESS SWITCH ON HEADLIGHT SWITCH THAT CONTROL DASH BRIGHTNESS AND IF BRIGHTNESS SWITCH IN FULL ON POSITION ON HEAD LIGHT SWITCH IT WILL CAUSE DOME LIGHT TO STAY ON.

The bright light dimmer switch will need replacing

That is normal. They go bright because during the daytime the outside light is also bright so the lights compensate for the outside brightness by making your dash lights also bright. When you turn your headlights on it assumes it is nighttime and you don't need to have the brightness to see the dash lights so it compensates for this. If you want them to be dimmer, near the light switch there is a roller button to turn your interior lights on just roll that some and it will either make the dash lights brighter or dimmer.

try checking the switch that turns normal lights to brights make sure there is no wire being grounded out

Your bright bulbs are probably burn out. And yes they can both burn out at the same time, its rare but not as rare as some think

the inner lights are the brights but some vehicles also use the bright lamps with low voltage as the daytime running lights