1998 Silverado---The daytime running lights come on whenever I start the truck. Whenever I turn the headlight switch to the ON position, the daytime light in the dash goes out but my dash lights and taillights do not illuminate. I have also been having problems with the dome light coming on whenever the door is open. Two separate problems, possibly related?

 

my dad had this problem with his dodge and the first time it was the fuse for the tail lights the second time it was the light switch its self in the dash.

 

check the switch, my dome light trigger on the drivers door is broken so it stays on if the door is shut, so even that can be an issue and also check the dome override button(i use that so my domes are off all the time) the day runnig lights are normal for 98's cause my old man has a 99 and it has thoes and the light should go off like you said tyours does when the lights are turned on by the switch.