It sounds like your dimmer control for your dash lights is set all the way
down. When I set mine all the way down ('04 2500HD) the dash lights will
still come back on when the dome light comes on.
If your dimmer isn't set all the way down, then it could be a faulty dimmer
switch. I don't know about your under-hood light, but that could be just a
bad bulb or dirt in the bulb socket.
Cheers - Jonathan
Don't know about your dash lights, but try giving the underhood
light a smack. GM uses a very stupid mechanical weight that
slides inside the light assembly to turn the light on. It usually
ends up sticking after awhile. I suppose the old mercury switches
are banned these days. If you carefully take the light apart, you
can see how it works and perhaps lube it up a bit. Personally,
I've never done that...we just replace the assembly.
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