Yes, your tail lights will go out when your dash board lights go out.
Are you sure you didn't turn the dimmer down
could be the alternator is about to go out
Alternator is failing.
If all the dash lights are out then there is two causes for this. The first is all the fuses have blown the other is the relay for the dashboard lights has went out.
Check for a loose ground wire - sounds like lights are backfeeding searching for ground
A likely cause is a faulty interior light dimming switch. This switch is directly connected to both the dash lights (for dimming), and the dome light (on/off).
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.
In most cars there is an dash light adjustment of some sort. My guess is yours is turned down too far so the lights don't show.
No. A bad battery is not causing your dash lights to go on and off. A different part is bad. Without equipment I have no idea what it is.
No the dash lights should be with your parking lights.comment2: They are on separate circuits. Power usually goes from the "taillight fuse" to a small 5 amp dash light fuse and then to the dash dimmer wheel or knob. Then it feeds the dash lights. A blown tail light fuse makes the dash lights go out also. A blown dash fuse only affects the dash lights.