Of course it's possible that the anti-theft module has been replaced at some point on a 25 year old car and the alarm code no longer matches the module...
Assuming that's not the case, if you open the remote case, with the remote held as you would to operate it, you will be able to see a potentiometer with a slot for a screwdriver on the front right of the remote. That's the tuning adjustment. You can use anything that doesn't conduct electricity to turn that pot (improvise) or turn and remove the screwdriver each time after an incremental adjustment before testing. The technique is to start at one end of the adjustment range and sweep across to the other end, operating the remote while observing the actuation (or not) of the anti-theft. The aim is to find where in the adjustment range the remote works and works best (maximum range).