[morzh]

Ok,

you have to pay attention to what you measure and from what pin to what pin.
You cannot measure part to part, you measure pin to pin.

For that matter, it makes no sense when you measure via GND. GND is solid wire.
Unless you specifically measure to make sure the GND is OK.

Now, when you say 6A7 pin 5, it is helpful when you add that it is the Control, or First, Grid and then C13 should not have any continuity to it, unless, again, you measure via GND which makes no sense as it serves no purpose.

Otherwise 6A7 Grid 1 to the Bandswitch (one pin of it) should indeed be a short and c13 (ungrounded pin going to one half of coil 16) to C14 should show continuity.