My daughter just bought a 99 buick century and neither the dash or the odometer/gear lights work? and the bright lite switch won't stay clicked into the bright position? Any ideas?

Try raising tilt steering wheel to highest position and clicking the high beams. If they come on and stay on then it's probably faulty turn signal switch. But that's only the high beam issue. Check to see if park lights work. If not then check fuse. This is for odo light issue.

As far as the gear selection lights I believe on yours they are controlled by a signal from your neutral safety switch. Might check harness connections to it. It's located right where linkage enters trans.

Did you try pushing the stalk the other way? One way, usually pulling towards you is spring loaded to flash you lights and will always return. If you push in, (or opposite of the way it won't stay) it might click in to position. Maybe try that

I bought my son a 1999 Century. Neither the odometer or the brights worked. After a week the low beams failed as well. I purchase the dash cluster on Ebay for 150.00 (40.00 refunded for CORE return) and put it in myself. Seriously took me 15 minutes after watching a Youtube video. The headlights were a little different. E bay part (Turn signal stem that controls the high/low beams, cruise, hazards and wipers for 40.00 bucks. Putting it in was a little tougher but not horrible. Had help from a friend with tools.

there are diodes on the back of the PCB instrument panel. Video shows how to replace the diodes saving about $100 plus time wasted waiting for the package. The Regal is similar, but gear shift is on the floor instead of on the column. https://www.youtube.com/watch? v=rtRINop3gE8