My sisters year 2000 JTD also has an airbag light. I have cleaned the connectors under the front seats but to no avail. If the fault has been fixed should the warning light go out automatically or could it need to be reset with appropriate software (eg fiatecuscan)
When my airbag warning LED came on, I just sprayed the contacts with electrolube and slid them off and on a few times to clean up the contacts. (connector is located under the front passenger seat) Never troubled me again.