You should not drink while on nafcillin (or any other antibiotic
for that matter).
One of the biggest reasons they tell you not to drink on
antibiotics is it puts too much stress on your liver.
If you've ever noticed that maybe you get intoxicated faster or
feel a 'different kind' of drunk while on antibiotics it is
basically your body freaking out over trying to keep yourself
healthy.
Antibiotics kill bacterial infections within us but that does
not mean that they are good for every part of the body, including
the liver. (hows that for a circular argument? Thanks biology)