Why is my right parking light not working

May be a bad connection in the globe holder, check that you have power and earth use a multi meter to check this.

My 1997 Buick lesabre's headlights,turn signals and brake lights all work but my tail lights do not, I checked the fuse and the bulb.

Check the headlight switch to make sure it is sending power to them. If it is, start at the tail lights and trace the wiring back to the switch to see where power is lost. It sounds like the lamp control module is out here is the location. Check out the diagrams (Below). Please let us know what you find. We are interested to see what it is.

I had this problem had to get a new LCM cost me $143.00 all fixed! I love this site.

Why my tail lights do not work, but my brake and signals do?

I am assuming that you have checked the bulbs and fuse for this. see picture the fuses and relay are under the rear seat fuse box. it can also be a module so if all is good then you need a mechanic to scan to see if it is a module problem.

Electrical problem
2000 Buick Lesabre 6 cyl Front Wheel Drive Automatic
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i just replaced the bulbs in my passenger side tail lights. the brake and blinker now works but the two bulbs in the running lights dont work. I suspct wiring or is there and inline fuse? Is this some thing a can plug a new harness in and be good or will i need to splice?

The rear running lights for both sides are on the same fuse. I would pull the whole tail light out and check the grounds. You will need to splice in order to change a socket, but it is not too hard if you do one wire at a time with the new socket. I would also try turning the bulbs around 180 as this occasionally works.