Airbag light stays on 2000 Lincoln LS

I had a similar problem with the air bag light and it turned out after testing the problem was a short in the wiring harness under the drivers seat. It aparently had a broken wire from the auto seat moving back and forth on entry and exit. It also has a memory for my wife and I and it also moves back and forth for that reason.
It has started to do it again and I found if I always start with the memory seat in #2 which closest to the steering wheel, {her setting}, then choose #1 setting it works normally. Crazy huh?
Just my experience!!!!!

Penomik is right have the dealer check it most likely its the sensor in the steering wheel let them deal with it.

I hate to say this is one of the few times I recommend taking your car to the dealer. Messing with the airbag system could cause it to deploy in your face, which believe me is not a pleasant experience. If it does deploy, the cost of a replacement will come close to the book value of the car. The other alternative would be that whatever you did to the airbag would case it not to deploy when you most need it. In either of these situations you are much better off throwing a few bills at the dealer.