On my 1991 Nissan pickup, the tail lights stay on even with ignition and light switch turned off. It's drained the battery so my only solution is to remove the bulbs. Any suggestions ?

My first guess is the ignition switch being faulty.
1st unplug the switch module and see if that turns the accessory lights off.
Test the ignition switch (on the switch side):
A. White , White Red wire is 12V constant
B. Blue/Red wire is accessories.
If there is continuity between these two wires when the ignition switch is OFF then replace it. $55.00 for the module.

tail light or BRAKE light ? if brake light replace the switch

Yes it sounds like the switch is stuck in the park position.
You could pull the harness plug for the switch and check the circuits with a meter, or replace the switch.

I suspect you have two separate issues your lights staying on is possibly a faulty stop and tail light bulb check both , I suspect you may also have a faulty starter motor.

you most likely have blown 10amp fuse for tail lights in the fuse box under the hood as far as tha tail lights go. turn your lights on and check your tail lights along with the plate lights. plate lights are on the same fuse as the tail lights. there is a fuse box by the battery which has tail light fuse in it. the lid of the fuse box is showing location of fuse. as far as your interior light goes, make sure that you have the switch in "door" position or it will not come on when door is opened. or just put it into "on" position to see if it comes on. but turn it off or put it back to "door" position/middle seting or your battery will drain down.

on ur brake pedal there is a brake light switch,if the plunger or adjustment is bad it will keep ur brake lights on,,,hoped it helped,,,

yes most definately.

your stater is out

there are 2 screws take them out get a putty knife andslightly put in between the tail light and bed jiggle it then pull firmly on light towards you chould come right out/Please rate my response thank you very much

hiya if the rear lights are remaining on ? with no ignition it will be the brake lights staying on this is easily remendied/ checked by trypulling the brake pedal up by hand and see if lights go off ? if so then you will need to adjust the b/light switch which is positioned adjacent to pedal and can be screwed inwards towards the pedal untill the plunger on switch is pushed into the switch which puts lights off ensure pedal is fully up then adjust switch reconnect the wire/plug and press pedal slightly to ensure b/lights operate ok and then go off with pedal released ? on hyundai the brakelights do not req ignition on to operate hence more likely problem is as above good luck