Are you sure they are both lighting?! I know on my Z that my tail light idiot light lights anytime I hit the brake (yes all my bulbs are OEM and it has plenty of fluid) but the light is so bright in the dash it LOOKS like my washer light is on too. However when my washer light REALLY comes on I can clearly see the difference. If you cant tell just by looking, drain your washer fluid and see if its any brighter.
Nissan just didnt do a good job preventing the light from one idiot light from bleeding into the others around it.