Yes, your tail lights will go out when your dash board lights go out.
Need to know what about the dash board lights.
When you say dimmer switch I assume you are refering to the internal dash-board lights dimmer switch. The dimmer switch for the dash-board lights is located on the speedometer panel.There are two black knobs that stick out between the warning lights on the dash. The right one is used to set the clock while the left one when rotated adjusts the dash-board lights and when depressed resets the odometer. This should be what you are looking for.
replacing dash board lights
Where is the Dash board lights fuse of ford mondeo 2002 lx
check your wiring for your lights under the dash or a bad ground
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do you have 2000 mazda 626 dash board?
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Check the dimmer setting for the dash lights. There should be a dial to adjust the brightness on the dash to the left of the steering wheel.
You may have a burnt out bulb that is causing your tail lights and dash board lights to not come on in your 1992 Bonneville. It can also be a blown fuse that is causing your problem.
It could be the dimmer switch that will adjust the dash lights