Chevrolet TrailBlazer Forum : “Rear Window Washer”

yes, they are supplied by the same resivoir with two seperate pumps.  the pump for the rear is located a little higher in the tank so as not to run you out of fluid for the front.  It's VERY common to have the lines become plugged, when i was working at one of the gm dealers here in town, i would get at least one a day that was plugged.  More than likely the lines are plugged or may have become disconnected.  if you can here the pump running (located passenger front of the engine compartment) then likely there is an issue with the line being plugged.  the best way to clean it out is using compressed air.