I have a 1999 jeep cherokee. 1 taillight out when head lights are on, on passenger side. All the bulbs (brake light bulb,reverse and blinker light bulb) on the problem taillight work individually just fine. since it is just one taillight and not both, is it less likely to be a problem within the light pull out switch, or could it be something else entirely?

So your taillights should have 2 bulbs in them. 1 that turns on when you turn your lights on and stays on until you turn them off. That same bulb should have a 2nd circuit that lights up when you press on your brakes. The 2nd bulb appears when your reverse gear is engaged. So if you have no lights on right you have to replace both bulbs and if you have no brake light on the left you just have to replace your rear brake light bulb.

check the bulbs in all the lights at the rear.make sure the right bulbs are in place if okay then check power at the light sockets with a test light.this should be a start.

Your right rear turn signal bulb is blown.Replace the bulb and the fast blinking will stop.

That problem is usually caused by a bad connection between the bulb socket and the tailamp housing. Take a look at the taillamp where the bulb socket screws in. If the lamp is warped due to overheating, you will need to replace that taillamp assembly.

If your brake light goes out when your headlights are on here is your fix:
1. remove taillight assembly (two screws hold it in place
2. Remove light bulb and socket from assembly (this will be the top bulb) put it to the side
3. Inside this hole on the rim you will see three silver metal contacts, two side by side and one by itself.
4. With a small screwdriver or a small pointed tool, gently pry up the contact which is by itself, all you are wanting to do is bend it upwards slightly.
Over the course of time this conact succumbs to the heat of the bulb and settles into the plastic. All you are doing now is making a better contact between the metal and the bulb.
DIY will cost you $0
This will fix your problem, it did mine and will save $200+ from a dealer.
GOOD FIXIN!

If your brake light goes out when your headlights are on here is your fix:
1. remove taillight assembly (two screws hold it in place
2. Remove light bulb and socket from assembly (this will be the top bulb) put it to the side
3. Inside this hole on the rim you will see three silver metal contacts, two side by side and one by itself.
4. With a small screwdriver or a small pointed tool, gently pry up the contact which is by itself, all you are wanting to do is bend it upwards slightly.
Over the course of time this conact succumbs to the heat of the bulb and settles into the plastic. All you are doing now is making a better contact between the metal and the bulb.
This will fix your problem, it did mine and will save $200+ from a dealer.
GOOD FIXIN!

check,by that i mean loosen remove clean/scrape ,the ground wire going to that tail light assembly . you should find it on the frame near wire harness plugs.

check brakelighy switch

First, I want to say thank you for the info, you saved me money and aggravation. Second it took mea little while to figure out what contact I was looking for. So I would like to provide a little more detail to make it easier for others in the future.
This is the corrective method for your brake lights not working when your headlights are on(2000 Jeep Cherokee Larado).
1) The cause of the problem is heat from the bulb.
2) Remove the light assembly as if you were going to change a bulb.
3) Turn the socket and remove it from the taillight assembly and set it aside(check to be sure your bulb is not burnt out).
4) Look at the opening, you will see 3 flat chrome colored contacts on the assembly.
5) Notice the one by it self at the top of the opening, that is the "ground".
6) If you look closely you will notice the plastic around the ground contact has shrunk a little bit, this caused the contact to pull away from the socket, causing the problem.
7) With a small flat head screwdriver, VERY GENTLY pry up the contact so it stays slightly upward by itself.
8) Re-insert the bulb assembly back into the housing and press your brake petal with your lights on.
9) You should be in good to go!
10) Tools: Phillips head screwdriver and a small flat head screwdriver.
11) Time : 5 minutes per light

have you checked the bulb sockets to see if they are burnt or corroded sometime i see that the plastic melts around the contacts where the socket twists into the housing. if your lucky you might get away with replacing just the socket for the brake/running light bulb. but if it is too melted your most likely going to need a new housing