I guess there could be continuity when the handles are down between red and black, but that doesn't really mean anything. I have never tried this on a transformer, mostly because it doesn't test anything. What you want to check with an AC volt meter set at a range of 50 volts is whether there is any voltage between red and black with the handles down. The fact that continuity briefly goes away when you raise the handle is likely due to the electronic circuit protection being energized.
The Z4000 is a complex transformer. A simple transformer would have continuity between red and black with the handle down because you would be reading one side of the transformer coil. The other side (coil) of the transformer would not be energized, so no voltage would pass with the handle down.
In any event, I don't understand what you are trying to test with a continuity tester on a Z4000. Without a full schematic and an understanding of electronic circuits, you aren't accomplishing anything.
George