Haha, so unsufficient washer fluid pressure is a fail, but almost 20 years old tires aren't...
Do it for your own safety then.
For the washer fluid, flush the reservoir first. Then check if the tube isn't bent or pressed somewhere. Had this on my girlfriend's car last year when we bought it, it was not used much for the previous 3 or 4 years. I found it by accident before it was its turn on the 'to do' list.