One headlight and all 3 tails stay on when car/switch is off

Question edited for clarity.
Question moved to model category.

tail lights don't need relays as the amperage is very low. Only headlights and fog lights use relays.

https://www.google.com/search?q=1993+Nissan+Pathfinder.+Where+is+the+tail+light+relay

Fuse Box diagram

https://www.google.com/search?q=1993+nissan+pathfinder+fuse+box+diagram

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Left light
Pink/black tail light
green/yellow stop light
grey/bue turn
black ground
Right
pink/black tail
green/yellow stop
grey/red turn
black ground

There is two or three different hookups for the pathfinder and the one you installed is not the right one

i know this sounds crazy, but do you have break/tail lights?some cars shut off dash lites when tail/brake lights dont work

need more ifo

The fuse should be located in the main chassis fuse panel, on the drivers side, beneath the dash area. Look for a removable panel of some sort. I believe the dash lights may be on the same circuit as your tail lights. If your tail lights still work, you might not have a blown fuse. Check to make sure you don't have the dimmer switch turned all the way down. A lot of people never use their dimmer switches and completely forget about them until the lights inadvertently get turned all the way down. If it's not the fuse or the dimmer, you may have a bad headlight switch or other wiring issue.

Check the grounding of ur headlight! rust or oxidation prevents current to light up ur BULB. Clean & check ur hedlight connector. Tell us wut happen if u done these helpfull hints!

If its just the lights, then probably the headlight switch. If radio problem is related then possibly a bad ignition switch.

Had a similar problem and fixed it by installing a new headlight switch / turn signal lever. Hope this helps.

good luck