Burned out headlight

It is located under the passenger side headlight assembly, behind the inner fender well skirt.

One of your left side parking lights is burned out. Good luck, Ned. The flasher works on resistance and the bulbs provide that redistance.

I would check the dealer for any TSBs

Raise your hood right behind your headlights you will see a cap twist off the cap turn to the left you will see the bulb snaps right out.

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

there's a possibility that it might be the socket that the bulb actually goes into. my break light did something similar to that. the socket only cost about 8 bucks from the dealer.

youtube.com type in 1998 grand cherokee headlight assembly, I just fixed mine in 10 minutes, both of them!

you need to change the coil on# 3

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

Why did you replace the switch without checking the headlight bulbs first? Suggest you check the headlight bulbs, if they are good, then check the connectors, if they are good, then check the fuse box. Sometimes there is a fuse for the healights right and left. If all of that is good check your ground connections. If all of that is good, then is to basics........check continuity on the harness, ensure there is current through the connector to the lights contact.

If all of athe above is good, then I always advise to check the fuse links. You might have burned one out. They are usually located near the battery.