The exterior lamp out warning light works on resistance changes. Some things can happen other than a burn out or removal to trigger the light:
If any exterior bulbs have been replaced with other than exact spec replacement bulbs that can cause the light to show.
Or you may have a bulb about to burn out. Any bulbs look extra bright?
Possibly a bulb has a corroded contact, causing a resistance change sufficient to trigger the warning light, but not enough to notice a change in the light output.
There may be other problems with the 90's cars that I am not aware of, but hope this sheds some additional light on the subject.