Nissan Quest 2004 Tail Lights

Blown fuse ,bad headlight switch,or wiring issue.
the tail lights have there own fuse and are powered through headlight switch. Do the front running lights come on? If none of them work, switch could be bad if front work and rears dont, check bulbs and power to them when lights are on

plastic tail light housings?

could be a faulty globe too

Start by replacing the light bulb.

there must be a short circuit which powers tail lights and brake lights. probably you have a dual filament bulbs which have both brake and tail light together. check for bulb, socket/or bulb housing and harness of that light.

in the rear lights you may have two bulbs one is the turn signal the other one is stop light / tail light the stop light / tail light has two filaments, one for the stop light (21 watt) & one for the tail light (5 watt) it is possible that the tail light filament is blown, try replacing the bulb to see if that fixes the problem,also check all the fuses as well.......hope this helps......cheers.

Bad brake light switch. It's just above your brake pedal under dash. Small plastic switch w/a couple of wires. Easy fix.

is it the tqail lmaps or stop lamp bulbs on?
If stop lamp bulbs, repalce the stop lamp switch on the brake pedal

tail lights work on a different filament than the rest of the lights you mentioned, it is possible both bulbs are burned out for that filament. if not, check the fuses as the tail light circuit in some cars is on a seperate fuse. the remaining possibility could be bad socket contacts.

The relay has nothing to do with the tail lights, but replacing the switch sounds like a good idea. There's a nut holding it in place, see http://www.skandix.de/en/spare-parts/electrics/switches/switch-headlight/1027524/ to get an idea of the construction. And the price. This is not worth fiddling about unreliable workarounds...
In addition, if fuses 15 and/or 16 burn frequently there might be a problem with the tail light cabling.

Good luck
Ingo