If the TII transmission was rebuilt, you have to correctly shim/depth the input shaft bearing. A replacement bearing can be a thou or two different from the previously installed one. If the input shaft sits too far forward, the face of the syncro lip on the input shaft will rub against the countershaft, making a whining noise. If it gets really bad, you can start chipping teeth. This rubbing would cause a whine while the input shaft is turning. The input shaft would turn when the clutch is engaged and the engine is driving the input shaft, or the input shaft would be back driven when the clutch is disengaged, but the transmission is in gear. If the clutch disengaged and the transmission is out of gear, the input shaft shouldn't be moving a whole lot.

Also check the countershaft for proper depth.

My $0.02, hope it helps